- 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
Buy this book
- About this book
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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
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Kunita was an invited speaker at the ICM 1986.
- Reviews
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“The presentation is self-contained, clear and precise. The book is definitely a must-read for researchers in the field of stochastic flows and stochastic differential equations.” (G. V. Riabov, Mathematical Reviews, October, 2020)
- Table of contents (7 chapters)
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Probability Distributions and Stochastic Processes
Pages 1-44
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Stochastic Integrals
Pages 45-75
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Stochastic Differential Equations and Stochastic Flows
Pages 77-124
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Diffusions, Jump-Diffusions and Heat Equations
Pages 125-166
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Malliavin Calculus
Pages 167-244
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Table of contents (7 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Stochastic Flows and Jump-Diffusions
- Authors
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- Hiroshi Kunita
- 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
