Stochastic Processes

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  • Format: Paperback
  • Copyright: 1999-06-01
  • Publisher: Society for Industrial & Applied
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This introductory textbook explains how and why probability models are applied to scientific fields such as medicine, biology, physics, oceanography, economics, and psychology to solve problems about stochastic processes. It does not just show how a problem is solved but explains why by formulating questions and first steps in the solutions. Stochastic Processes is ideal for a course aiming to give examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models. It introduces the methods of probability model building and provides the reader with mathematically sound techniques as well as the ability to further study the theory of stochastic processes. Originally published in 1962, this was the first comprehensive survey of stochastic processes requiring only a minimal background in introductory probability theory and mathematical analysis. Stochastic Processes continues to be unique, with many topics and examples still not discussed in other textbooks.

Author Biography

Emanuel Parzen is Distinguished Professor of Statistics at Texas AandM University

Table of Contents

Preface to the Classics Editionp. xiii
Prefacep. xvii
Role of the Theory of Stochastic Processes
Statistical physicsp. 1
Stochastic models for population growthp. 2
Communication and controlp. 2
Management sciencep. 4
Time series analysisp. 5
Random Variables and Stochastic Processes
Random variables and probability lawsp. 8
Describing the probability law of a stochastic processp. 22
The Wiener process and the Poisson processp. 26
Two-valued processesp. 35
Conditional Probability and Conditional Expectation
Conditioning by a discrete random variablep. 42
Conditioning by a continuous random variablep. 51
Properties of conditional expectationp. 62
Normal Processes and Covariance Stationary Processes
The mean value function and covariance kernel of a stochastic processp. 66
Stationary and evolutionary processesp. 69
Integration and differentiation of stochastic processesp. 78
Normal processesp. 88
Normal processes as limits of stochastic processesp. 97
Harmonic analysis of stochastic processesp. 103
Counting Processes and Poisson Processes
Axiomatic derivations of the Poisson processp. 118
Non-homogeneous, generalized, and compound Poisson processesp. 124
Inter-arrival times and waiting timesp. 132
The uniform distribution of waiting times of a Poisson processp. 139
Filtered Poisson processesp. 144
Renewal Counting Processes
Examples of renewal counting processesp. 160
The renewal equationp. 170
Limit theorems for renewal counting processesp. 180
Markov Chains: Discrete Parameter
Formal definition of a Markov processp. 188
Transition probabilities and the Chapman-Kolmogorov equationp. 193
Decomposition of Markov chains into communicating classesp. 208
Occupation times and first passage timesp. 211
Recurrent and non-recurrent states and classesp. 221
First passage and absorption probabilitiesp. 226
Mean absorption, first passage, and recurrence timesp. 238
Long-run and stationary distributionsp. 247
Limit theorems for occupation timesp. 265
Limit theorems for transition probabilities of a finite Markov chainp. 270
The interchange of limiting processesp. 273
Markov Chains: Continuous Parameter
Limit theorems for transition probabilities of a continuous parameter Markov chainp. 276
Birth and death processes and their application to queueing theoryp. 278
Kolmogorov differential equations for the transition probability functionsp. 288
Two-state Markov chains and pure birth processesp. 293
Non-homogeneous birth and death processesp. 299
Referencesp. 307
Author Indexp. 314
Subject Indexp. 316
Table of Contents provided by Syndetics. All Rights Reserved.

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