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Stochastic Processes

A Survey of the Mathematical Theory

  • Book
  • © 1977

Overview

Authors:
  1. John Lamperti

    1. Department of Mathematics, Dartmouth College, Hanover, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 23)

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Table of contents (10 chapters)

  1. Front Matter

    Pages N1-xvii
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  2. General Introduction

    • John Lamperti
    Pages 1-11

  3. Second-Order Random Functions

    • John Lamperti
    Pages 12-31

  4. Stationary 2nd-Order Processes

    • John Lamperti
    Pages 32-51

  5. Interpolation and Prediction

    • John Lamperti
    Pages 52-82

  6. Strictly-Stationary Processes and Ergodic Theory

    • John Lamperti
    Pages 83-105

  7. Markov Transition Functions

    • John Lamperti
    Pages 106-133

  8. The Application of Semigroup Theory

    • John Lamperti
    Pages 134-180

  9. Markov Processes

    • John Lamperti
    Pages 181-203

  10. Strong Markov Processes

    • John Lamperti
    Pages 204-233

  11. Martingale Theory

    • John Lamperti
    Pages 234-249

  12. Back Matter

    Pages 250-267
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Keywords

About this book

This book is the result of lectures which I gave dur­ ing the academic year 1972-73 to third-year students a~ Aarhus University in Denmark. The purpose of the book, as of the lectures, is to survey some of the main themes in the modern theory of stochastic processes. In my previous book Probability: ! survey of the mathe­ matical theory I gave a short overview of "classical" proba­ bility mathematics, concentrating especially on sums of inde­ pendent random variables. I did not discuss specific appli­ cations of the theory; I did strive for a spirit friendly to application by coming to grips as fast as I could with the major problems and techniques and by avoiding too high levels of abstraction and completeness. At the same time, I tried to make the proofs both rigorous and motivated and to show how certain results have evolved rather than just presenting them in polished final form. The same remarks apply to this book, at least as a statement of intentions, and it can serve as a sequel to the earlier one continuing the story in the same style and spirit. The contents of the present book fall roughly into two parts. The first deals mostly with stationary processes, which provide the mathematics for describing phenomena in a steady state overall but subject to random fluctuations. Chapter 4 is the heart of this part.

Authors and Affiliations

  • Department of Mathematics, Dartmouth College, Hanover, USA

    John Lamperti

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