Probability and Stochastics

  • Erhan Çinlar

Part of the Graduate Texts in Mathematics book series (GTM, volume 261)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Erhan Çınlar
    Pages 1-47
  3. Erhan Çınlar
    Pages 49-92
  4. Erhan Çınlar
    Pages 93-137
  5. Erhan Çınlar
    Pages 139-170
  6. Erhan Çınlar
    Pages 172-242
  7. Erhan Çınlar
    Pages 243-312
  8. Erhan Çınlar
    Pages 313-377
  9. Erhan Çınlar
    Pages 379-441
  10. Erhan Çınlar
    Pages 443-542
  11. Back Matter
    Pages 533-557

About this book

Introduction

This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form.

 

The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes.

Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. 

 

The book is based on the author’s lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics.

 

Erhan Çinlar has received many awards for excellence in teaching, including the President’s Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.

Keywords

Bessel processes Brownian motion Levy processes Poisson processes stochastic processes

Authors and affiliations

  • Erhan Çinlar
    • 1
  1. 1.Princeton UniversityPrincetonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-87859-1
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-87858-4
  • Online ISBN 978-0-387-87859-1
  • Series Print ISSN 0072-5285
  • About this book