Stochastic Flows And Jump Diffusions
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Stochastic Flows and Jump diffusions
Author | : H. Kunita |
Publsiher | : Unknown |
Total Pages | : 352 |
Release | : 2019 |
Genre | : Electronic books |
ISBN | : 9811338027 |
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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.
Stochastic Flows and Jump Diffusions
Author | : Hiroshi Kunita |
Publsiher | : Springer |
Total Pages | : 352 |
Release | : 2019-03-26 |
Genre | : Mathematics |
ISBN | : 9789811338014 |
Download Stochastic Flows and Jump Diffusions Book in PDF, Epub and Kindle
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.
Stochastic Flows and Stochastic Differential Equations
Author | : Hiroshi Kunita,H. Kunita |
Publsiher | : Cambridge University Press |
Total Pages | : 364 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 0521599253 |
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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.
Applied Stochastic Control of Jump Diffusions
Author | : Bernt Øksendal,Agnès Sulem |
Publsiher | : Springer Science & Business Media |
Total Pages | : 263 |
Release | : 2007-04-26 |
Genre | : Mathematics |
ISBN | : 9783540698265 |
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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
Diffusion Processes and Related Problems in Analysis
Author | : Mark A. Pinsky |
Publsiher | : Springer Science & Business Media |
Total Pages | : 0 |
Release | : 1992 |
Genre | : Diffusion processes |
ISBN | : 0817635432 |
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Applied Stochastic Processes and Control for Jump Diffusions
Author | : Floyd B. Hanson |
Publsiher | : SIAM |
Total Pages | : 472 |
Release | : 2007-01-01 |
Genre | : Mathematics |
ISBN | : 0898718635 |
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This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems.
On the Geometry of Diffusion Operators and Stochastic Flows
Author | : K.D. Elworthy,Yves Le Jan,Xue-Mei Li |
Publsiher | : Springer Verlag |
Total Pages | : 140 |
Release | : 1999-11-17 |
Genre | : Mathematics |
ISBN | : UOM:39015043098881 |
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This book constitutes the refereed proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery, DGCI'99 held in Marne-la-Vallee, France in March 1999. The 24 revised full papers presented were selected from a total of 41 submissions. Also included are four invited papers and seven poster presentations. The volume is divided in topical sections on discrete objects and shapes, planes, surfaces, reconstruction, topology, distance and object recognition, thinning, discretization and visualization.
On the Geometry of Diffusion Operators and Stochastic Flows
Author | : K. D. Elworthy,Y. Le Jan,Xue-Mei Li |
Publsiher | : Unknown |
Total Pages | : 112 |
Release | : 2014-09-01 |
Genre | : Electronic Book |
ISBN | : 3662203464 |
Download On the Geometry of Diffusion Operators and Stochastic Flows Book in PDF, Epub and Kindle