Advertisement

Basics of Applied Stochastic Processes

  • Richard Serfozo

Part of the Probability and Its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Richard Serfozo
    Pages 1-98
  3. Richard Serfozo
    Pages 99-167
  4. Richard Serfozo
    Pages 169-239
  5. Richard Serfozo
    Pages 241-340
  6. Richard Serfozo
    Pages 341-404
  7. Richard Serfozo
    Pages 405-425
  8. Back Matter
    Pages 427-443

About this book

Introduction

Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters. Although these results differ for various processes, they have a common trait of being limit theorems for processes with regenerative increments. Extensive examples and exercises show how to formulate stochastic models of systems as functions of a system’s data and dynamics, and how to represent and analyze cost and performance measures. Topics include stochastic networks, spatial and space-time Poisson processes, queueing, reversible processes, simulation, Brownian approximations, and varied Markovian models.

The technical level of the volume is between that of introductory texts that focus on highlights of applied stochastic processes, and advanced texts that focus on theoretical aspects of processes. Intended readers are researchers and graduate students in mathematics, statistics, operations research, computer science, engineering, and business.

Keywords

60-02, 60-J10, 60-J27, 60-K05, 60-J25 Brownian motion Markov chain Poisson process continuous-time Markov chain regenerative process stochastic network stochastic process

Authors and affiliations

  • Richard Serfozo
    • 1
  1. 1.Georgia Institute of TechnologySchool of Industrial & Systems EngineeringAtlantaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-89332-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-89331-8
  • Online ISBN 978-3-540-89332-5
  • Series Print ISSN 1431-7028
  • Buy this book on publisher's site