---

＜電子ブック＞
Stochastic Flows and Jump-Diffusions / by Hiroshi Kunita
(Probability Theory and Stochastic Modelling. ISSN:21993149 ; 92)

版	1st ed. 2019.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2019
本文言語	英語
大きさ	XVII, 352 p. 145 illus : online resource
著者標目	*Kunita, Hiroshi author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Social sciences -- Mathematics  全ての件名で検索 LCSH:Differential equations FREE:Probability Theory FREE:Mathematics in Business, Economics and Finance FREE:Differential Equations
一般注記	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 heatequations are constructed independently of the theory of partial differential equations. Researchers and graduate student in probability theory will find this book very useful HTTP:URL=https://doi.org/10.1007/978-981-13-3801-4

 類似資料