Lecture Notes in Mathematics
cover

Stochastic Analysis in Discrete and Continuous Settings

With Normal Martingales

Authors: Privault, Nicolas

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-642-02380-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
About this book

This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.

Reviews

From the reviews:

“The author presents several aspects of stochastic analysis for discrete and continuous-time normal martingales. … variety of operators on the Poisson space is an highlight of this book. … It is finally worth mentioning that this volume of the Lecture Notes in Mathematics includes many interesting applications and that the various notions, properties and proofs are clear and detailed.” (A. Réveillac, Zentralblatt MATH, Vol. 1185, 2010)

“The book under review has the original feature of giving a unified treatment to all normal martingales. … The book is quite accessible to beginners. … its main goal is providing advanced researchers with a study of stochastic analysis in both discrete and continuous time and with a simultaneous treatment of both continuous and jump processes.” (Dominique Lépingle, Mathematical Reviews, Issue 2011 j)


Table of contents (10 chapters)

Table of contents (10 chapters)
  • Introduction

    Pages 1-6

    Privault, Nicolas

  • The Discrete Time Case

    Pages 7-58

    Privault, Nicolas

  • Continuous Time Normal Martingales

    Pages 59-112

    Privault, Nicolas

  • Gradient and Divergence Operators

    Pages 113-130

    Privault, Nicolas

  • Annihilation and Creation Operators

    Pages 131-160

    Privault, Nicolas

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-642-02380-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Stochastic Analysis in Discrete and Continuous Settings
Book Subtitle
With Normal Martingales
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1982
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-02380-4
DOI
10.1007/978-3-642-02380-4
Softcover ISBN
978-3-642-02379-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVI, 282
Topics