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Stochastic Flows and Jump-Diffusions

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Stochastic Flows and Jump-Diffusions/ by Hiroshi Kunita.
Author:	Kunita, Hiroshi.
Description:	XVII, 352 p. 145 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Probabilities. -
Online resource:	https://doi.org/10.1007/978-981-13-3801-4
ISBN:	9789811338014

Stochastic Flows and Jump-Diffusions
Kunita, Hiroshi.

Stochastic Flows and Jump-Diffusions[electronic resource] /by Hiroshi Kunita. - 1st ed. 2019. - XVII, 352 p. 145 illus.online resource. - Probability Theory and Stochastic Modelling,922199-3130 ;. - Probability Theory and Stochastic Modelling,76.

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.

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.

ISBN: 9789811338014

Standard No.: 10.1007/978-981-13-3801-4doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Stochastic Flows and Jump-Diffusions
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520 $a 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.
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