Skip to main content
SpringerLink
Log in

Stochastic Analysis in Discrete and Continuous Settings

With Normal Martingales

  • Book
  • © 2009

Overview

Authors:
  1. Nicolas Privault

    1. Dept. Mathematics, City University of Hong Kong, Hong Kong, Hong Kong/PR China

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1982)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages 1-7
    Download chapter PDF

  2. Introduction

    • Nicolas Privault
    Pages 1-6

  3. The Discrete Time Case

    • Nicolas Privault
    Pages 7-58

  4. Continuous Time Normal Martingales

    • Nicolas Privault
    Pages 59-112

  5. Gradient and Divergence Operators

    • Nicolas Privault
    Pages 113-130

  6. Annihilation and Creation Operators

    • Nicolas Privault
    Pages 131-160

  7. Analysis on the Wiener Space

    • Nicolas Privault
    Pages 161-194

  8. Analysis on the Poisson Space

    • Nicolas Privault
    Pages 195-246

  9. Local Gradients on the Poisson Space

    • Nicolas Privault
    Pages 247-280

  10. Option Hedging in Continuous Time

    • Nicolas Privault
    Pages 281-293

  11. Appendix

    • Nicolas Privault
    Pages 295-300

  12. Back Matter

    Pages 1-15
    Download chapter PDF
Back to top

Keywords

About this book

This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.

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)

Authors and Affiliations

  • Dept. Mathematics, City University of Hong Kong, Hong Kong, Hong Kong/PR China

    Nicolas Privault

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation