Introduction to Malliavin calculus

Author(s)

Bibliographic Information

Introduction to Malliavin calculus

David Nualart, Eulalia Nualart

(Institute of Mathematical Statistics textbooks, 9)

Cambridge University Press, 2018

  • : pbk

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Note

Includes bibliographical references (p. 228-233) and index

Description and Table of Contents

Description

This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Levy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.

Table of Contents

  • Preface
  • 1. Brownian motion
  • 2. Stochastic calculus
  • 3. Derivative and divergence operators
  • 4. Wiener chaos
  • 5. Ornstein-Uhlenbeck semigroup
  • 6. Stochastic integral representations
  • 7. Study of densities
  • 8. Normal approximations
  • 9. Jump processes
  • 10. Malliavin calculus for jump processes I
  • 11. Malliavin calculus for jump processes II
  • Appendix A. Basics of stochastic processes
  • References
  • Index.

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