Stochastic Processes

A Survey of the Mathematical Theory

  • John Lamperti

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

Table of contents

  1. Front Matter
    Pages N1-xvii
  2. John Lamperti
    Pages 1-11
  3. John Lamperti
    Pages 12-31
  4. John Lamperti
    Pages 32-51
  5. John Lamperti
    Pages 52-82
  6. John Lamperti
    Pages 106-133
  7. John Lamperti
    Pages 134-180
  8. John Lamperti
    Pages 181-203
  9. John Lamperti
    Pages 204-233
  10. John Lamperti
    Pages 234-249
  11. Back Matter
    Pages 250-267

About this book

Introduction

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.

Keywords

Markov process Markowscher Prozess Martingale Stationärer Prozess Stochastic processes Stochastischer Prozess random function stochastic process

Authors and affiliations

  • John Lamperti
    • 1
  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9358-0
  • Copyright Information Springer-Verlag New York 1977
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90275-3
  • Online ISBN 978-1-4684-9358-0
  • Series Print ISSN 0066-5452
  • About this book