# Stochastic Processes

## A Survey of the Mathematical Theory

Book

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

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 83-105
7. John Lamperti
Pages 106-133
8. John Lamperti
Pages 134-180
9. John Lamperti
Pages 181-203
10. John Lamperti
Pages 204-233
11. John Lamperti
Pages 234-249
12. Back Matter
Pages 250-267

### 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

1. 1.Department of MathematicsDartmouth CollegeHanoverUSA

### Bibliographic information

• Book Title Stochastic Processes
• Book Subtitle A Survey of the Mathematical Theory
• Authors J. Lamperti
• Series Title Applied Mathematical Sciences
• 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
• Softcover ISBN 978-0-387-90275-3
• eBook ISBN 978-1-4684-9358-0
• Series ISSN 0066-5452
• Edition Number 1
• Number of Pages , 288
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site