An Introduction to Stochastic Processes

by Edward P.C. Kao

Overview

A vigorous response to the challenges of incorporating computer use into the teaching and learning of stochastic processes, this book takes an applications- and computer-oriented approach rather than the standard formal and mathematically rigorous approach. It is suitable for advanced undergraduates and beginning graduate students in operations research, management science, finance, engineering, statistics, computer science, and applied mathematics. Prerequisites are intermediate-level calculus, elementary linear algebra, and an introductory course in probability with an emphasis in operational skills on conditioning. 
The first chapter reviews some preliminary materials, including transform methods and basic concepts in mathematical analysis. Subsequent chapters explore variants of Poisson processes, renewal processes, discrete-time and continuous-time Markov chains, Markov renewal and semi-regenerative processes, and Brownian motion and other diffusion processes. Each chapter concludes with problems, bibliographic notes, references, and an Appendix. A Solutions Manual is available to instructors upon request.

Product Details

ISBN-13:	9780486837925
Publisher:	Dover Publications
Publication date:	12/18/2019
Series:	Dover Books on Mathematics
Pages:	448
Sales rank:	1,097,424
Product dimensions:	5.90(w) x 8.90(h) x 0.90(d)

About the Author

Edward P. C. Kao is Professor of Mathematics at the University of Houston.

Table of Contents

1. INTRODUCTION Overview / Introduction / Discrete Random Variables and Generating Functions / Continuous Random Variables and Laplace Transforms / Some Mathematical Background / Problems / Bibliographic Notes / References /

Appendix
2.POISSON PROCESSES Overview / Introduction / Properties of Poisson Processes / Nonhomogeneous Poisson Processes / Filtered Poisson Processes / Two-Dimensional and Marked Poisson Processes / Poisson Arrivals See Time Averages (PASTA) / Problems / Bibliographic Notes / References /

Appendix
3.RENEWAL PROCESSES Overview / Introduction / Renewal-Type Equations / Excess Life, Current Life, and Total Life / Renewal Reward Processes / Limiting Theorems, Stationary and Transient Renewal Processes / Regenerative Processes / Discrete Renewal Processes / Problems / Bibliographic Notes / References /

Appendix
4.DISCRETE-TIME MARKOV CHAINS Overview / Introduction / Classification of States / Ergodic and Periodic Markov Chains / Absorbing Markov Chains / Markov Reward Processes / Reversible Discrete-Time Markov Chains / Problems / Bibliographic Notes / References /

Appendix
5.CONTINUOUS-TIME MARKOV CHAINS Overview / Introduction / The Kolmogorov Differential Equations / The Limiting Probabilities / Absorbing Continuous-Time Markov Chains / Phase-Type Distributions / Uniformization / Continuous-Time Markov Reward Processes / Reversible Continuous-Time Markov Chains / Problems / Bibliographic Notes / References /

Appendix
6.MARKOV RENEWAL AND SEMI-REGENERATIVE PROCESSES Overview / Introduction / Markov Renewal Functions and Equations / Semi-Markov Processes and Related Reward Processes /Semi-Regenerative Processes / Problems / Bibliographic Notes / References /

Appendix
7.BROWNIAN MOTION AND OTHER DIFFUSION PROCESSES Overview / Introduction / Diffusion Processes / Ito's Calculus and Stochastic Differential Equations / Multidimensional Ito's Lemma / Control of Systems of Stochastic Differential Equations / Problems / Bibliographic Notes / References /

Appendix / APPENDIX: GETTING STARTED WITH MATLAB / INDEX