What is included with this book?
Preface to the Classics Edition | p. xiii |
Preface | p. xvii |
Role of the Theory of Stochastic Processes | |
Statistical physics | p. 1 |
Stochastic models for population growth | p. 2 |
Communication and control | p. 2 |
Management science | p. 4 |
Time series analysis | p. 5 |
Random Variables and Stochastic Processes | |
Random variables and probability laws | p. 8 |
Describing the probability law of a stochastic process | p. 22 |
The Wiener process and the Poisson process | p. 26 |
Two-valued processes | p. 35 |
Conditional Probability and Conditional Expectation | |
Conditioning by a discrete random variable | p. 42 |
Conditioning by a continuous random variable | p. 51 |
Properties of conditional expectation | p. 62 |
Normal Processes and Covariance Stationary Processes | |
The mean value function and covariance kernel of a stochastic process | p. 66 |
Stationary and evolutionary processes | p. 69 |
Integration and differentiation of stochastic processes | p. 78 |
Normal processes | p. 88 |
Normal processes as limits of stochastic processes | p. 97 |
Harmonic analysis of stochastic processes | p. 103 |
Counting Processes and Poisson Processes | |
Axiomatic derivations of the Poisson process | p. 118 |
Non-homogeneous, generalized, and compound Poisson processes | p. 124 |
Inter-arrival times and waiting times | p. 132 |
The uniform distribution of waiting times of a Poisson process | p. 139 |
Filtered Poisson processes | p. 144 |
Renewal Counting Processes | |
Examples of renewal counting processes | p. 160 |
The renewal equation | p. 170 |
Limit theorems for renewal counting processes | p. 180 |
Markov Chains: Discrete Parameter | |
Formal definition of a Markov process | p. 188 |
Transition probabilities and the Chapman-Kolmogorov equation | p. 193 |
Decomposition of Markov chains into communicating classes | p. 208 |
Occupation times and first passage times | p. 211 |
Recurrent and non-recurrent states and classes | p. 221 |
First passage and absorption probabilities | p. 226 |
Mean absorption, first passage, and recurrence times | p. 238 |
Long-run and stationary distributions | p. 247 |
Limit theorems for occupation times | p. 265 |
Limit theorems for transition probabilities of a finite Markov chain | p. 270 |
The interchange of limiting processes | p. 273 |
Markov Chains: Continuous Parameter | |
Limit theorems for transition probabilities of a continuous parameter Markov chain | p. 276 |
Birth and death processes and their application to queueing theory | p. 278 |
Kolmogorov differential equations for the transition probability functions | p. 288 |
Two-state Markov chains and pure birth processes | p. 293 |
Non-homogeneous birth and death processes | p. 299 |
References | p. 307 |
Author Index | p. 314 |
Subject Index | p. 316 |
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