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1. Perturbed semiMarkov type processes. I, Limit theorems for rareevent times and processes [2022]
 Silʹvestrov, D. S. (Dmitriĭ Sergeevich), author.
 Cham : Springer, [2022]
 Description
 Book — 1 online resource (xvii, 401 pages) : illustrations (some color)
 Summary

 Preface. List of symbols. Introduction. Part I: FirstRareEvent Times for Regularly Perturbed SemiMarkov Processes. Flows of Rare Events for Regularly Perturbed SemiMarkov Processes. Generalizations of Limit Theorems for FirstRareEvent Times. FirstRareEvent Times for Perturbed Risk Processes. FirstRareEvent Times for Perturbed Closed Queuing Systems. FirstRareEvent Times for Perturbed M/MType Queuing Systems. Part II: Hitting Times and Phase Space Reduction for Perturbed SemiMarkov Processes. Asymptotically Comparable Functions. Perturbed SemiMarkov Processes and Reduction of Phase Space. Asymptotics of Hitting Times for Perturbed SemiMarkov Processes. Asymptotics for Expectations of Hitting Times for Perturbed SemiMarkov Processes. Generalizations and Examples of Limit Theorems for Hitting Times. Limit Theorems for Randomly Stopped Stochastic Processes. Methodological and Bibliographical Notes. References. Index.
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 CocozzaThivent, Christiane, author.
 Cham : Springer, [2021]
 Description
 Book — 1 online resource : illustrations (some color)
 Summary

 Tools. Markov renewal processes and related processes. First steps with PDMP. Hitting time distribution. Intensity of some marked point pocesses. Generalized Kolmogorov equations. A martingale approach. Stability. Numerical methods. Switching Processes. Tools. Interarrival distribution with several Dirac measures. Algorithm convergence's proof.
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 Pogorui, Anatoliy, author.
 London : ISTE, Ltd. ; Hoboken, NJ : Wiley, 2021.
 Description
 Book — 1 online resource
 Summary

 Preface ix
 Acknowledgments xiii
 Introduction xv
 Part 1. Basic Methods 1
 Chapter 1. Preliminary Concepts 3
 1.1. Introduction to random evolutions 3
 1.2. Abstract potential operators 7
 1.3. Markov processes: operator semigroups 11
 1.4. SemiMarkov processes 14
 1.5. Lumped Markov chains 17
 1.6. Switched processes in Markov and semiMarkov media 19
 Chapter 2. Homogeneous Random Evolutions (HRE) and their Applications 23
 2.1. Homogeneous random evolutions (HRE) 24
 2.1.1. Definition and classification of HRE 24
 2.1.2. Some examples of HRE 25
 2.1.3. Martingale characterization of HRE 28
 2.1.4. Analogue of Dynkin's formula for HRE 34
 2.1.5. Boundary value problems for HRE 36
 2.2. Limit theorems for HRE 37
 2.2.1. Weak convergence of HRE 37
 2.2.2. Averaging of HRE 39
 2.2.3. Diffusion approximation of HRE 42
 2.2.4. Averaging of REs in reducible phase space: merged HRE 45
 2.2.5. Diffusion approximation of HRE in reducible phase space 48
 2.2.6. Normal deviations of HRE 51
 2.2.7. Rates of convergence in the limit theorems for HRE 53
 Part 2. Applications to Reliability, Random Motions, and Telegraph Processes 57
 Chapter 3. Asymptotic Analysis for Distributions of Markov, SemiMarkov and Random Evolutions 59
 3.1. Asymptotic distribution of time to reach a level that is infinitely increasing by a family of semiMarkov processes on the set ? 61
 3.2. Asymptotic inequalities for the distribution of the occupation time of a semiMarkov process in an increasing set of states 74
 3.3. Asymptotic analysis of the occupation time distribution of an embedded semiMarkov process (with increasing states) in a diffusion process 77
 3.4. Asymptotic analysis of a semigroup of operators of the singularly perturbed random evolution in semiMarkov media 82
 3.5. Asymptotic expansion for distribution of random motion in Markov media under the Kac condition 90
 3.5.1. The equation for the probability density of the particle position performing a random walk in ?n 90
 3.5.2. Equation for the probability density of the particle position 91
 3.5.3. Reduction of a singularly perturbed evolution equation to a regularly perturbed equation 93
 3.6. Asymptotic estimation for application of the telegraph process as an alternative to the diffusion process in the BlackScholes formula 96
 3.6.1. Asymptotic expansion for the singularly perturbed random evolution in Markov media in case of disbalance 96
 3.6.2. Application to an economic model of stock market 100
 Chapter 4. Random Switched Processes with Delay in Reflecting Boundaries 103
 4.1. Stationary distribution of evolutionary switched processes in a Markov environment with delay in reflecting boundaries 104
 4.2. Stationary distribution of switched process in semiMarkov media with delay in reflecting barriers 109
 4.2.1. Infinitesimal operator of random evolution with semiMarkov switching 110
 4.2.2. Stationary distribution of random evolution in semiMarkov media with delaying boundaries in balance case 113
 4.2.3. Stationary distribution of random evolution in semiMarkov media with delaying boundaries 121
 4.3. Stationary efficiency of a system with two unreliable subsystems in cascade and one buffer: the Markov case 124
 4.3.1. Introduction 124
 4.3.2. Stationary distribution of Markov stochastic evolutions 125
 4.3.3. Stationary efficiency of a system with two unreliable subsystems in cascade and one buffer 129
 4.3.4. Mathematical model 131
 4.3.5. Main mathematical results 133
 4.3.6. Numerical results for the symmetric case 138
 4.4. Application of random evolutions with delaying barriers to modelling control of supply systems with feedback: the semiMarkov switching process 141
 4.4.1. Estimation of stationary efficiency of onephase system with a reservoir 141
 4.4.2. Estimation of stationary efficiency of a production system with two unreliable supply lines 149
 Chapter 5. Onedimensional Random Motions in Markov and SemiMarkov Media 159
 5.1. Onedimensional semiMarkov evolutions with general Erlang sojourn times 160
 5.1.1. Mathematical model 160
 5.1.2. Solution of PDEs with constant coefficients and derivability of functions ranged in commutative algebras 168
 5.1.3. Infinitedimensional case 171
 5.1.4. The distribution of onedimensional random evolutions in Erlang media 172
 5.2. Distribution of limiting position of fading evolution 181
 5.2.1. Distribution of random power series in cases of uniform and Erlang distributions 182
 5.2.2. The distribution of the limiting position 190
 5.3. Differential and integral equations for jump random motions 191
 5.3.1. The Erlang jump telegraph process on a line 192
 5.3.2. Examples 198
 5.4. Estimation of the number of level crossings by the telegraph process 199
 5.4.1. Estimation of the number of level crossings for the telegraph process in Kac's condition 202
 References 205
 Index 219
 Summary of Volume 2 221.
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(source: Nielsen Book Data)
 Pogorui, Anatoliy.
 London : ISTE Ltd. ; Hoboken, NJ : Wiley, 2021.
 Description
 Book — 1 online resource
 Summary

 Preface ix
 Acknowledgments xiii
 Introduction xv
 Part 1. Higherdimensional Random Motions and Interactive Particles 1
 Chapter 1. Random Motions in Higher Dimensions 3
 1.1. Random motion at finite speed with semiMarkov switching directions process 5
 1.1.1. ErlangKdistributed direction alternations 7
 1.1.2. Some properties of the random walk in a semiMarkov environment and its characteristic function 15
 1.2. Random motion with uniformly distributed directions and random velocity 17
 1.2.1. Renewal equation for the characteristic function of isotropic motion with random velocity in a semiMarkov media 17
 1.2.2. Onedimensional case 20
 1.2.3. Twodimensional case 23
 1.2.4. Threedimensional case 23
 1.2.5. Fourdimensional case 31
 1.3. The distribution of random motion at nonconstant velocity in semiMarkov media 32
 1.3.1. Renewal equation for the characteristic function 34
 1.3.2. Twodimensional case 35
 1.3.3. Threedimensional case 37
 1.3.4. Fourdimensional case 40
 1.4. GoldsteinKac telegraph equations and random flights in higher dimensions 43
 1.4.1. Preliminaries about our modeling approach 45
 1.4.2. Twodimensional case 48
 1.4.3. Threedimensional case 51
 1.4.4. Fivedimensional case 59
 1.5. The jump telegraph process in Rn 62
 1.5.1. The jump telegraph process in R3 63
 1.5.2. Conclusions and final remarks 64
 Chapter 2. System of Interactive Particles with Markov and SemiMarkov Switching 67
 2.1. Description of the Markov model 68
 2.1.1. Distribution of the first meeting time of two telegraph processes 69
 2.1.2. Estimate of the number of particle collisions 74
 2.1.3. Free path times of a family of particles 76
 2.1.4. Estimation of the number of particle collisions for systems with boundaries 78
 2.1.5. Estimation of the number of particle collisions for systems without boundaries 83
 2.2. Interaction of particles governed by generalized integrated telegraph processes: a semiMarkov case 87
 2.2.1. Laplace transform of the distribution of the first collision of two particles 88
 2.2.2. SemiMarkov case 91
 2.2.3. Distribution of the first collision of two particles with finite expectation 95
 Part 2. Financial Applications 99
 Chapter 3. Asymptotic Estimation for Application of the Telegraph Process as an Alternative to the Diffusion Process in the BlackScholes Formula 101
 3.1. Asymptotic expansion for the singularly perturbed random evolution in Markov media in the case of disbalance 101
 3.2. Application: BlackScholes formula 106
 Chapter 4. Variance, Volatility, Covariance and Correlation Swaps for Financial Markets with Markovmodulated Volatilities 111
 4.1. Volatility derivatives 111
 4.1.1. Types of volatilities 111
 4.1.2. Models for volatilities 113
 4.1.3. Variance and volatility swaps 115
 4.1.4. Covariance and correlation swaps 116
 4.1.5. A brief literature review 117
 4.2. Martingale representation of a Markov process 118
 4.3. Variance and volatility swaps for financial markets with Markovmodulated stochastic volatilities 122
 4.3.1. Pricing variance swaps 124
 4.3.2. Pricing volatility swaps 124
 4.4. Covariance and correlation swaps for two risky assets for financial markets with Markovmodulated stochastic volatilities 128
 4.4.1. Pricing covariance swaps 128
 4.4.2. Pricing correlation swaps 130
 4.4.3. Correlation swap made simple 130
 4.5. Example: variance, volatility, covariance and correlation swaps for stochastic volatility driven by two state continuous Markov chain 132
 4.6. Numerical example 134
 4.6.1. S&P 500: variance and volatility swaps 134
 4.6.2. S&P 500 and NASDAQ100: covariance and correlation swaps 135
 4.7. Appendix 1 138
 4.7.1. Correlation swaps: firstorder correction 138
 Chapter 5. Modeling and Pricing of Variance, Volatility, Covariance and Correlation Swaps for Financial Markets with SemiMarkov Volatilities 143
 5.1. Introduction 143
 5.2. Martingale representation of semiMarkov processes 148
 5.3. Variance and volatility swaps for financial markets with semiMarkov stochastic volatilities 151
 5.3.1. Pricing of variance swaps 153
 5.3.2. Pricing of volatility swaps 155
 5.3.3. Numerical evaluation of variance and volatility swaps with semiMarkov volatility 158
 5.4. Covariance and correlation swaps for two risky assets in financial markets with semiMarkov stochastic volatilities 159
 5.4.1. Pricing of covariance swaps 160
 5.4.2. Pricing of correlation swaps 162
 5.5. Numerical evaluation of covariance and correlation swaps with semiMarkov stochastic volatility 164
 5.6. Appendices 165
 5.6.1. Appendix 1. Realized correlation: firstorder correction 165
 5.6.2. Appendix 2. Discussions of some extensions 169
 References 177
 Index 191
 Summary of Volume 1 193.
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 Brémaud, Pierre.
 2nd ed.  Cham : Springer, 2020.
 Description
 Book — 1 online resource (564 pages)
 Summary

 Preface. 1 Probability Review. 2 DiscreteTime Markov Chains. 3 Recurrence and Ergodicity. 4 LongRun Behavior. 5 DiscreteTime Renewal Theory. 6 Absorption and Passage Times. 7 Lyapunov Functions and Martingales. 8 Random Walks on Graphs. 9 Convergence Rates. 10 Markov Fields on Graphs. 11 Monte Carlo Markov Chains. 12 Nonhomogeneous Markov Chains. 13 ContinuousTime Markov Chains. 14 Markovian Queueing Theory. Appendices. Bibliography. Index.
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 Grabski, Franciszek, author.
 First edition.  Waltham, MA : Elsevier, [2015]
 Description
 Book — 1 online resource (1 volume) : illustrations
 Summary

 PREFACE NOTATIONS LIST OF FIGURES LIST OF TABLES 1.RANDOM PROCESS 2.DISCRETE STATE SPACE MARKOV PROCESSES 3.SEMIMARKOV PROCESS 4.CHARACTERISTICS OF SEMIMARKOV PROCESS 5.PERTURBED SEMIMARKOV PROCESSES 6.STOCHASTIC PROCESSES ASSOCIATED WITH SEMIMARKOV PROCESS 7.MODELS OF RENEWABLE COLD STANDBY SYSTEM WITH REPAIR 8.SEMIMARKOV MODELS OF MULTISTAGE OPERATION 9.SEMIMARKOV MODEL OF WORKING RATE PROCESS 10.MULTITASK OPERATION PROCESS 11.SEMIMARKOV FAILURE RATE PROCESS 12.MODEL OF RENEWABLE SERIES SYSTEM 13.SIMPLE MODELS OF MAINTENANCE 14.MULTISTATE PROCESS OF SYSTEM DAMAGE 15.MULTISTATE SYSTEM WITH SEMIMARKOV COMPONENTS 16.SEMIMARKOV MAINTENANCE NET 17.SEMIMARKOV DECISION PROCESSES 18.APPENDIX SUMMARY BIBLIOGRAPHY.
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 Brémaud, Pierre.
 2ieme éd., entièrement révisée.  Berlin : Springer, ©2009.
 Description
 Book — 1 online resource (viii, 309 pages) : illustrations
 Summary

 Introduction
 1 La notion de probabilité.2 Variables aléatoires discrètes
 2 Vecteurs aléatoires
 4 Espérance conditionnelle
 5 Information et entropie.
 6 L'espérance comme intégrale
 7 Suites de variablesaléatoires
 8 Chaînes de Markov
 Solutions des exercices.Bibliographie
 Index.
 Montenegro, Ravi R.
 Boston, MA : Now Publishers, ©2006.
 Description
 Book — ix, 121 pages : illustrations ; 24 cm
 Summary

 1 Introduction 2 Basic Bounds on Mixing Times 3 Advanced Functional Techniques 4 Evolving Set Methods 5 Lower Bounds on Mixing Times and their Consequences 6 Examples 7 Miscellaneous 8 Open Problems Acknowledgements References Appendix.
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SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

Stacks  Request (opens in new tab) 
QA274.7 .M665 2006  Available 
 Modica, Giuseppe.
 Chichester : Wiley, 2013.
 Description
 Book — 1 online resource
 Summary

 Preface xi
 1 Combinatorics 1 1.1 Binomial coefficients 1 1.1.1 Pascal triangle 1 1.1.2 Some properties of binomial coefficients 2 1.1.3 Generalized binomial coefficients and binomial series 3 1.1.4 Inversion formulas 4 1.1.5 Exercises 6 1.2 Sets, permutations and functions 8 1.2.1 Sets 8 1.2.2 Permutations 8 1.2.3 Multisets 10 1.2.4 Lists and functions 11 1.2.5 Injective functions 12 1.2.6 Monotone increasing functions 12 1.2.7 Monotone nondecreasing functions 13 1.2.8 Surjective functions 14 1.2.9 Exercises 16 1.3 Drawings 16 1.3.1 Ordered drawings 16 1.3.2 Simple drawings 17 1.3.3 Multiplicative property of drawings 17 1.3.4 Exercises 18 1.4 Grouping 19 1.4.1 Collocations of pairwise different objects 19 1.4.2 Collocations of identical objects 22 1.4.3 Multiplicative property 23 1.4.4 Collocations in statistical physics 24 1.4.5 Exercises 24
 2 Probability measures 27 2.1 Elementary probability 28 2.1.1 Exercises 29 2.2 Basic facts 33 2.2.1 Events 34 2.2.2 Probability measures 36 2.2.3 Continuity of measures 37 2.2.4 Integral with respect to a measure 39 2.2.5 Probabilities on finite and denumerable sets 40 2.2.6 Probabilities on denumerable sets 42 2.2.7 Probabilities on uncountable sets 44 2.2.8 Exercises 46 2.3 Conditional probability 51 2.3.1 Definition 51 2.3.2 Bayes formula 52 2.3.3 Exercises 54 2.4 Inclusion exclusion principle 60 2.4.1 Exercises 63
 3 Random variables 68 3.1 Random variables 68 3.1.1 Definitions 69 3.1.2 Expected value 75 3.1.3 Functions of random variables 77 3.1.4 Cavalieri formula 80 3.1.5 Variance 82 3.1.6 Markov and Chebyshev inequalities 82 3.1.7 Variational characterization of the median and of the expected value 83 3.1.8 Exercises 84 3.2 A few discrete distributions 91 3.2.1 Bernoulli distribution 91 3.2.2 Binomial distribution 91 3.2.3 Hypergeometric distribution 93 3.2.4 Negative binomial distribution 94 3.2.5 Poisson distribution 95 3.2.6 Geometric distribution 98 3.2.7 Exercises 101 3.3 Some absolutely continuous distributions 102 3.3.1 Uniform distribution 102 3.3.2 Normal distribution 104 3.3.3 Exponential distribution 106 3.3.4 Gamma distributions 108 3.3.5 Failure rate 110 3.3.6 Exercises 111
 4 Vector valued random variables 113 4.1 Joint distribution 113 4.1.1 Joint and marginal distributions 114 4.1.2 Exercises 117 4.2 Covariance 120 4.2.1 Random variables with finite expected value and variance 120 4.2.2 Correlation coefficient 123 4.2.3 Exercises 123 4.3 Independent random variables 124 4.3.1 Independent events 124 4.3.2 Independent random variables 127 4.3.3 Independence of many random variables 128 4.3.4 Sum of independent random variables 130 4.3.5 Exercises 131 4.4 Sequences of independent random variables 140 4.4.1 Weak law of large numbers 140 4.4.2 Borel Cantelli lemma 142 4.4.3 Convergences of random variables 143 4.4.4 Strong law of large numbers 146 4.4.5 A few applications of the law of large numbers 152 4.4.6 Central limit theorem 159 4.4.7 Exercises 163
 5 Discrete time Markov chains 168 5.1 Stochastic matrices 168 5.1.1 Definitions 169 5.1.2 Oriented graphs 170 5.1.3 Exercises 172 5.2 Markov chains 173 5.2.1 Stochastic processes 173 5.2.2 Transition matrices 174 5.2.3 Homogeneous processes 174 5.2.4 Markov chains 174 5.2.5 Canonical Markov chains 178 5.2.6 Exercises 181 5.3 Some characteristic parameters 187 5.3.1 Steps for a first visit 187 5.3.2 Probability of (at least) r visits 189 5.3.3 Recurrent and transient states 191 5.3.4 Mean first passage time 193 5.3.5 Hitting time and hitting probabilities 195 5.3.6 Exercises 198 5.4 Finite stochastic matrices 201 5.4.1 Canonical representation 201 5.4.2 States classification 203 5.4.3 Exercises 205 5.5 Regular stochastic matrices 206 5.5.1 Iterated maps 206 5.5.2 Existence of fixed points 209 5.5.3 Regular stochastic matrices 210 5.5.4 Characteristic parameters 218 5.5.5 Exercises 220 5.6 Ergodic property 222 5.6.1 Number of steps between consecutive visits 222 5.6.2 Ergodic theorem 224 5.6.3 Powers of irreducible stochastic matrices 226 5.6.4 Markov chain Monte Carlo 228 5.7 Renewal theorem 233 5.7.1 Periodicity 233 5.7.2 Renewal theorem 234 5.7.3 Exercises 239
 6 An introduction to continuous time Markov chains 241 6.1 Poisson process 241 6.2 Continuous time Markov chains 246 6.2.1 Definitions 246 6.2.2 Continuous semigroups of stochastic matrices 248 6.2.3 Examples of rightcontinuous Markov chains 256 6.2.4 Holding times 259 Appendix A Power series 261 A.1 Basic properties 261 A.2 Product of series 263 A.3 Banach space valued power series 264 A.3.2 Exercises 267 Appendix B Measure and integration 270 B.1 Measures 270 B.1.1 Basic properties 270 B.1.2 Construction of measures 272 B.1.3 Exercises 279 B.2 Measurable functions and integration 279 B.2.1 Measurable functions 280 B.2.2 The integral 283 B.2.3 Properties of the integral 284 B.2.4 Cavalieri formula 286 B.2.5 Markov inequality 287 B.2.6 Null sets and the integral 287 B.2.7 Push forward of a measure 289 B.2.8 Exercises 290 B.3 Product measures and iterated integrals 294 B.3.1 Product measures 294 B.3.2 Reduction formulas 296 B.3.3 Exercises 297 B.4 Convergence theorems 298 B.4.1 Almost everywhere convergence 298 B.4.2 Strong convergence 300 B.4.3 Fatou lemma 301 B.4.4 Dominated convergence theorem 302 B.4.5 Absolute continuity of integrals 305 B.4.6 Differentiation of the integral 305 B.4.7 Weak convergence of measures 308 B.4.8 Exercises 312 Appendix C Systems of linear ordinary differential equations 313 C.1 Cauchy problem 313 C.1.1 Uniqueness 313 C.1.2 Existence 315 C.2 Efficient computation of eQt 317 C.2.1 Similarity methods 317 C.2.2 Putzer method 319 C.3 Continuous semigroups 321 References 324 Index 327.
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 Markov Anniversary Meeting (2006 : Charleston, S.C.)
 Raleigh, N.C. : Boson Books, ©2006.
 Description
 Book — 1 online resource
 Summary

 Preface; Program Committee;
 1. Seneta;
 2. Burrage et. al.;
 3. Cloth and Haverkort;
 4. Marie;
 5. Latouche;
 6. Spaey, Houdt and Blondia;
 7. Vuuren and Adan;
 8. Tian and Perros;
 9. Dopper, Gaujal and Vincent;
 10. Horvath and Telek;
 11. Hilgers and Langville;
 12. Da Silva and Rubino;
 13. Mamoun, Busic, Fourneau and Pekergin;
 14. Dayar et. al.;
 15. Langville and Meyer;
 16. Benzi and Ucar;
 17. Tancrez and Semal;
 18. Kirkland;
 19. Dayar;
 20. Sbeity and Plateau;
 21. Kumar;
 22. Caswell.
 Chung, Kai Lai, 19172009.
 2d ed.  Berlin, New York, Springer, 1967.
 Description
 Book — 1 online resource (x, 301 pages) Digital: text file.PDF.
 Summary

 I. Discrete Parameter
 § 1. Fundamental definitions
 § 2. Transition probabilities
 § 3. Classification of states
 § 4. Recurrence
 § 5. Criteria and examples
 § 6. The main limit theorem
 § 7. Various complements
 § 8. Repetitive pattern and renewal process
 § 9. Taboo probabilities
 § 10. The generating function
 § 11. The moments of first entrance time distributions
 § 12. A random walk example
 § 13. System theorems
 § 14. Functionals and associated random variables
 § 15. Ergodic theorems
 § 16. Further limit theorems
 § 17. Almost closed and sojourn sets
 II. Continuous Parameter
 § 1. Transition matrix: basic properties
 § 2. Standard transition matrix
 § 3. Differentiability
 § 4. Definitions and measuretheoretic foundations
 § 5. The sets of constancy
 § 6. Continuity properties of sample functions
 § 7. Further specifications of the process
 § 8. Optional random variable
 § 9. Strong Markov property
 § 10. Classification of states
 § 11. Taboo probability functions
 § 12. Last exit time
 § 13. Ratio limit theorems; discrete approximations
 § 14. Functionals
 § 15. Postexit process
 § 16. Imbedded renewal process
 § 17. The two systems of differential equations
 § 18. The minimal solution
 § 19. The first infinity
 § 20. Examples.
 Tveito, Aslak, 1961 author.
 Switzerland : SpringerOpen, 2016.
 Description
 Book — 1 online resource (xvi, 261 pages) : illustrations (some color)
 Summary

 Background : problem and methods
 Onedimensional calcium release
 Models of open and state blockers
 Properties of probability density functions
 Twodimensional calcium release
 Computing theoretical drugs in the twodimensional case
 Generalized systems governing probability density functions
 Calciuminduced calcium release
 Numerical drugs for calciuminduced calcium release
 A prototypical model of an ion channel
 Inactivated ion channels : extending the prototype model
 A simple model of the sodium channel
 Mutations affecting the mean open time
 The burst mode of the mutant sodium channel
 Action potentials : summing up the effect of loads of ion channels.
 Silʹvestrov, D. S. (Dmitriĭ Sergeevich), author.
 Cham : Springer, [2022]
 Description
 Book — 1 online resource : illustrations (some color)
 Summary

 Preface. List of symbols. Introduction. Part I: Ergodic Theorems for Perturbed Alternating Regenerative Processes. Ergodic Theorems for Perturbed Regenerative Processes. Perturbed Alternating Regenerative Processes. Ergodic Theorems for Regularly Perturbed Alternating Regenerative Processes. Ergodic Theorems for Regularly Perturbed Alternating Regenerative Processes Compressed in Time. SuperLong and Long Time Ergodic Theorems for Singularly Perturbed Alternating Regenerative Processes. Short Time Ergodic Theorems for Singularly Perturbed Alternating Regenerative Processes. Ergodic Theorems for Singularly Perturbed Alternating Regenerative Processes Compressed in Time. Ergodic Theorems for SuperSingularly Perturbed Alternating Regenerative Processes. Part II: Ergodic Theorems for Perturbed MultiAlternating Regenerative Processes. Perturbed MultiAlternating Regenerative Processes. TimeSpace Aggregation of Regeneration Times for Perturbed MultiAlternating Regenerative Processes. Embedded Processes for Perturbed MultiAlternating Regenerative Processes. Ergodic Theorems for Perturbed MultiAlternating Regenerative Processes. Perturbed Renewal Equation. Supplementary Asymptotic Results. Methodological and Bibliography Notes. References. Index. .
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14. Markov processes for stochastic modeling [2013]
 Ibe, Oliver C. (Oliver Chukwudi), 1947 author.
 Second edition.  London : Elsevier, 2013.
 Description
 Book — 1 online resource (xviii, 494 pages).
 Summary

 Chapter 1: Basic Concepts
 Chapter 2: Introduction to Markov Processes
 Chapter 3: DiscreteTime Markov Chains
 Chapter 4: ContinuousTime Markov Chains
 Chapter 5: Markovian Queueing Systems
 Chapter 6: Markov Renewal Processes
 Chapter 7: Markovian Arrival Processes
 Chapter 8: Random Walk
 Chapter 9: Brownian Motion and Diffusion Processes
 Chapter 10: Controlled Markov Processes
 Chapter 11: Hidden Markov Models
 Chapter 12: Markov Point Processes.
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 Mustererkennung mit MarkovModellen. English
 Fink, Gernot A.
 Berlin ; New York : Springer, 2008.
 Description
 Book — xii, 248 p. : ill. ; 24 cm.
 Summary

 1. Introduction1.1 Thematic Context1.2 Capabilities of Markov Models1.3 Goal and Structure
 2. Application Areas2.1 Speech2.2 Handwriting2.3 Biological Sequences2.4 Outlook Part I: Theory
 3. Foundations of Mathematical Statistics3.1 Experiment, Event, and Probability3.2 Random Variables and Probability Distributions3.3 Parameters of Probability Distributions3.4 Normal Distributions and Mixture Density Models3.5 Stochastic Processes and Markov Chains3.6 Principles of Parameter Estimation3.7 Bibliographical Remarks
 4. Vector Quantisation4.1 Definition4.2 Optimality4.3 Algorithms for Vector Quantiser Design (LLoyd, LBG, kmeans)4.4 Estimation of Mixture Density Models4.5 Bibliographical Remarks
 5. HiddenMarkov Models5.1 Definition5.2 Modeling of Output Distributions5.3 UseCases5.4 Notation5.5 Scoring (Forward algorithm)5.6 Decoding (Viterbi algorithm)5.7 Parameter Estimation (Forwardbackward algorithm, BaumWelch, Viterbi, and segmental kmeans training)5.8 Model Variants5.9 Bibliographical Remarks
 6. nGram Models6.1 Definition6.2 UseCases6.3 Notation6.4 Scoring6.5 Parameter Estimation (discounting, interpolation and backingoff)6.6 Model Variants (categorial models, longdistance dependencies)6.7 Bibliographical Remarks Part II: Practical Aspects
 7. Computations with Probabilities7.1 Logarithmic Probability Representation7.2 Flooring of Probabilities7.3 Codebook Evaluation in TiedMixture Models7.4 Likelihood Ratios
 8. Configuration of HiddenMarkov Models8.1 Model Topologies8.2 SubModel Units8.3 Compound Models8.4 ProfileHMMs8.5 Modelling of Output Probability Densities
 9. Robust Parameter Estimation9.1 Optimization of Feature Representations (Principle component analysis, whitening, linear discriminant analysis)9.2 Tying (of model parameters, especially: mixture tying)9.3 Parameter Initialization
 10. Efficient Model Evaluation10.1 Efficient Decoding of Mixture Densities10.2 Beam Search10.3 Efficient Parameter Estimation (forwardbackward pruning, segmental BaumWelch, training of model hierarchies)10.4 Treebased Model Representations
 11. Model Adaptation11.1 Foundations of Adaptation11.2 Adaptation of HiddenMarkov Models (Maximumlikelihood linear regression)11.3 Adaptation of nGram Models (cache models, dialogstep dependent models, topicbased language models)
 12. Integrated Search12.1 HMM Networks12.2 Multipass Search Strategies12.3 SearchSpace Copies (context and timebased tree copying strategies, language model lookahead)12.4 Timesynchronous Integrated Decoding Part III: Putting it All Together
 13. Speech Recognition13.1 ApplicationSpecific Processing (feature extraction, vocal tract length normalization, ...)13.2 Systems (e.g. BBN Byblos, SPHINX III, ...)
 14. Text Recognition14.1 ApplicationSpecific Processing (linearization of data representation for offline applications, preprocessing, normalization, feature extraction)14.2 Systems for Online Handwriting Recognition14.3 Systems for Offline Handwriting Recognition
 15. Analysis of Biological Sequences15.1 Representation of Biological Sequences15.2 Systems (HMMer, SAM, MetaMEME).
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Engineering Library (Terman)
Engineering Library (Terman)  Status 

Stacks  
Q327 .F5613 2008  Unknown 
 Gardner, Robert B., author.
 London, UK : Academic Press, an imprint of Elsevier, 2022.
 Description
 Book — 1 online resource.
 Summary

Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory. Here, not only Extremal Problems and Inequalities of MarkovBernstein Type for Algebraic Polynomials, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory.
 MinjárezSosa, J. Adolfo.
 Cham : Springer, 2020.
 Description
 Book — 1 online resource Digital: text file.PDF.
 Summary

 Zerosum Markov games. Discounted optimality criterion. Average payoff criterion. Empirical approximationestimation algorithms in Markov games. Differenceequation games: examples. Elements from analysis. Probability measures and weak convergence. Stochastic kernels. Review on density estimation. .
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
18. Prócessus de Markov [1967]
 Meyer, Paul André.
 Berlin ; New York : SpringerVerlag, 1967.
 Description
 Book — 1 online resource (189 pages)
 Summary

 Theorie elementaire des processus de markov
 Semigroupes de feller
 Processus de hunt, processus standard
 Reduites, mesures harmoniques.
 Delmas, JeanFrançois.
 Berlin ; New York : Springer, ©2006.
 Description
 Book — 1 online resource (xv, 431 pages) : illustrations Digital: text file.PDF.
 Summary

 Chaînes de Markov à temps discret
 Recuit simulé
 Gestions des approvisionnements
 Le processus de GaltonWatson
 Recherche de zones homogènes dans l'ADN
 Séquences exceptionnelles dans l'ADN
 Estimation du taux de mutation de l'ADN
 Chaînes de Markov à temps continu
 Files d'attente
 Éléments de fiabilité
 Lois de valeurs extrêmes
 Processus de coagulation et fragmentation.
20. An introduction to Markov processes [2014]
 Stroock, Daniel W., author.
 Second edition.  Berlin ; New York : Springer, 2014.
 Description
 Book — 1 online resource (xvii, 203 pages) Digital: text file.PDF.
 Summary

 Preface. Random Walks, a Good Place to Begin. Doeblin's Theory for Markov Chains. Stationary Probabilities. More about the Ergodic Theory of Markov Chains. Markov Processes in Continuous Time. Reversible Markov Processes. A minimal Introduction to Measure Theory. Notation. References. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
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