Skip to main content
  • Textbook
  • © 1993

An Introduction to Probability and Stochastic Processes

Authors:

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

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-2726-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)

This is a preview of subscription content, access via your institution.

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
  2. Univariate Random Variables

    • Marc A. Berger
    Pages 1-26
  3. Multivariate Random Variables

    • Marc A. Berger
    Pages 27-44
  4. Limit Laws

    • Marc A. Berger
    Pages 45-77
  5. Markov Chains—Passage Phenomena

    • Marc A. Berger
    Pages 78-100
  6. Markov Jump Processes

    • Marc A. Berger
    Pages 121-138
  7. Ergodic Theory with an Application to Fractals

    • Marc A. Berger
    Pages 139-172
  8. Back Matter

    Pages 173-206

About this book

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

  • School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Marc A. Berger

Bibliographic Information

  • Book Title: An Introduction to Probability and Stochastic Processes

  • Authors: Marc A. Berger

  • Series Title: Springer Texts in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-2726-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1993

  • Softcover ISBN: 978-1-4612-7643-2

  • eBook ISBN: 978-1-4612-2726-7

  • Series ISSN: 1431-875X

  • Series E-ISSN: 2197-4136

  • Edition Number: 1

  • Number of Pages: XII, 205

  • Topics: Probability Theory

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-2726-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)