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An Introduction to Probability and Stochastic Processes

  • Marc A. Berger

Part of the Springer Texts in Statistics book series (STS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Marc A. Berger
    Pages 1-26
  3. Marc A. Berger
    Pages 27-44
  4. Marc A. Berger
    Pages 45-77
  5. Marc A. Berger
    Pages 78-100
  6. Marc A. Berger
    Pages 121-138
  7. Marc A. Berger
    Pages 139-172
  8. Back Matter
    Pages 173-206

About this book

Introduction

These notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabilistically" whenever possible without recourse to other branches of mathematics and in a notation that is as "probabilistic" as possible. Thus, for example, the asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron­ Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com­ putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem.

Keywords

Ergodic theory Law of large numbers Markov chain Normal distribution Poisson process Random variable Stochastic processes ergodicity jump process stochastic process

Authors and affiliations

  • Marc A. Berger
    • 1
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-2726-7
  • Copyright Information Springer-Verlag New York 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7643-2
  • Online ISBN 978-1-4612-2726-7
  • Series Print ISSN 1431-875X
  • Buy this book on publisher's site