Stochastic flows and jump-diffusions
Author(s)
Bibliographic Information
Stochastic flows and jump-diffusions
（Probability theory and stochastic modelling, v. 92）
Springer, c2019
Available at / 17 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
KUN||14||1200039109038
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Note
Includes bibliographical references (p. 341-345) and indexes
Description and Table of Contents
Description
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.
Table of Contents
Preface.- Introduction.- 1.Probability distributions and stochastic processes.- 2.Stochastic integrals based on Wiener processes and Poisson random measures.- 3.Stochastic differential equations and stochastic flows.- 4.Diffusions, jump-diffusions and heat equations.- 5.Malliavin calculus for Wiener processes and Poisson random measures.- 6.Smooth densities and heat kernels.- 7.Jump-diffusions on manifolds and smooth densities.- Bibliography.- Index.
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