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Stochastic Flows and Stochastic Differential Equations

1990 Mathematics
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Release : 1990
Genre : Mathematics
Kind : eBook
Book Rating : 252/5 ( reviews)

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Book Synopsis Stochastic Flows and Stochastic Differential Equations by : Hiroshi Kunita

Download or read book Stochastic Flows and Stochastic Differential Equations written by Hiroshi Kunita. This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations and stochastic flow of diffeomorphisms, and through the former to study the properties of stochastic flows.The classical theory was initiated by K. Itô and since then has been much developed. Professor Kunita's approach here is to regard the stochastic differential equation as a dynamical system driven by a random vector field, including thereby Itô's theory as a special case. The book can be used with advanced courses on probability theory or for self-study.

An Introduction to the Geometry of Stochastic Flows

2004 Mathematics
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Release : 2004
Genre : Mathematics
Kind : eBook
Book Rating : 817/5 ( reviews)

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Book Synopsis An Introduction to the Geometry of Stochastic Flows by : Fabrice Baudoin

Download or read book An Introduction to the Geometry of Stochastic Flows written by Fabrice Baudoin. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a self-contained introduction to the local geometry of the stochastic flows associated with stochastic differential equations. It stresses the view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry whose main tools are introduced throughout the text. By using the connection between stochastic flows and partial differential equations, we apply this point of view of the study of hypoelliptic operators written in Hormander's form.

Stochastic Flows and Jump-Diffusions

2019-03-26 Mathematics
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Release : 2019-03-26
Genre : Mathematics
Kind : eBook
Book Rating : 019/5 ( reviews)

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Book Synopsis Stochastic Flows and Jump-Diffusions by : Hiroshi Kunita

Download or read book Stochastic Flows and Jump-Diffusions written by Hiroshi Kunita. This book was released on 2019-03-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Stochastic Flows and Applications

1986 Flows (Differentiable dynamical systems).
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Release : 1986
Genre : Flows (Differentiable dynamical systems).
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Lectures on Stochastic Flows and Applications by : H. Kunita

Download or read book Lectures on Stochastic Flows and Applications written by H. Kunita. This book was released on 1986. Available in PDF, EPUB and Kindle. Book excerpt:

Diffusion Processes and Related Problems in Analysis, Volume II

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 899/5 ( reviews)

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Book Synopsis Diffusion Processes and Related Problems in Analysis, Volume II by : V. Wihstutz

Download or read book Diffusion Processes and Related Problems in Analysis, Volume II written by V. Wihstutz. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.

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