Probability Theory and Stochastic Modelling

Stochastic Flows and Jump-Diffusions

Authors: Kunita, Hiroshi

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  • Provides systematic treatment of the Malliavin calculus on the Wiener–Poisson space, introducing Sobolev norms
  • Uses the flow property of the solution of stochastic differential equations and application to dual jump-diffusions
  • Is a study of fundamental solutions through stochastic analysis without the aid of partial differential equations
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  • ISBN 978-981-13-3801-4
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About this book

This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps.In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations.Researchers and graduate student in probability theory will find this book very useful.

About the authors

Kunita was an invited speaker at the ICM 1986. 

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Probability Distributions and Stochastic Processes

    Pages 1-44

    Kunita, Hiroshi

  • Stochastic Integrals

    Pages 45-75

    Kunita, Hiroshi

  • Stochastic Differential Equations and Stochastic Flows

    Pages 77-124

    Kunita, Hiroshi

  • Diffusions, Jump-Diffusions and Heat Equations

    Pages 125-166

    Kunita, Hiroshi

  • Malliavin Calculus

    Pages 167-244

    Kunita, Hiroshi

Buy this book

eBook n/a
  • ISBN 978-981-13-3801-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-981-13-3800-7
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Flows and Jump-Diffusions
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
92
Copyright
2019
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-13-3801-4
DOI
10.1007/978-981-13-3801-4
Hardcover ISBN
978-981-13-3800-7
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XVII, 352
Number of Illustrations
145 b/w illustrations
Topics