Stochastic Flows And Jump Diffusions
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Stochastic Flows And Jump Diffusions
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Author : H. Kunita
language : en
Publisher:
Release Date : 2019
Stochastic Flows And Jump Diffusions written by H. Kunita and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Electronic books categories.
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
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Author : Hiroshi Kunita
language : en
Publisher: Springer
Release Date : 2019-03-26
Stochastic Flows And Jump Diffusions written by Hiroshi Kunita and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-26 with Mathematics categories.
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.
Diffusion Processes And Related Problems In Analysis
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Author : Mark A. Pinsky
language : en
Publisher: Springer Science & Business Media
Release Date : 1992
Diffusion Processes And Related Problems In Analysis written by Mark A. Pinsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Diffusion processes categories.
On The Geometry Of Diffusion Operators And Stochastic Flows
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Author : K. D. Elworthy
language : en
Publisher:
Release Date : 2014-09-01
On The Geometry Of Diffusion Operators And Stochastic Flows written by K. D. Elworthy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
On The Geometry Of Diffusion Operators And Stochastic Flows
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Author : K.D. Elworthy
language : en
Publisher: Springer Verlag
Release Date : 1999-11-17
On The Geometry Of Diffusion Operators And Stochastic Flows written by K.D. Elworthy and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-17 with Mathematics categories.
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.
Stochastic Flows And Stochastic Differential Equations
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Author : Hiroshi Kunita
language : en
Publisher: Cambridge University Press
Release Date : 1990
Stochastic Flows And Stochastic Differential Equations written by Hiroshi Kunita and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
Lectures On Stochastic Flows And Applications
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Author : H. Kunita
language : en
Publisher:
Release Date : 1986
Lectures On Stochastic Flows And Applications written by H. Kunita and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Flows (Differentiable dynamical systems). categories.
Stochastic Flows In The Brownian Web And Net
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Author : Emmanuel Schertzer
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-01-08
Stochastic Flows In The Brownian Web And Net written by Emmanuel Schertzer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-08 with Mathematics categories.
It is known that certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments have diffusive scaling limits. Here, in the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was first developed by Le Jan and Raimond, who showed that each such flow is characterized by its -point motions. The authors' work focuses on a class of stochastic flows of kernels with Brownian -point motions which, after their inventors, will be called Howitt-Warren flows. The authors' main result gives a graphical construction of general Howitt-Warren flows, where the underlying random environment takes on the form of a suitably marked Brownian web. This extends earlier work of Howitt and Warren who showed that a special case, the so-called "erosion flow", can be constructed from two coupled "sticky Brownian webs". The authors' construction for general Howitt-Warren flows is based on a Poisson marking procedure developed by Newman, Ravishankar and Schertzer for the Brownian web. Alternatively, the authors show that a special subclass of the Howitt-Warren flows can be constructed as random flows of mass in a Brownian net, introduced by Sun and Swart. Using these constructions, the authors prove some new results for the Howitt-Warren flows.
Applied Stochastic Control Of Jump Diffusions
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Author : Bernt Øksendal
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-26
Applied Stochastic Control Of Jump Diffusions written by Bernt Øksendal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-26 with Mathematics categories.
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 Jump Processes And Stochastic Differential Equations
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Author : Wojbor Andrzej Woyczyński
language : en
Publisher: CRC Press
Release Date : 2021-11-23
Diffusion Processes Jump Processes And Stochastic Differential Equations written by Wojbor Andrzej Woyczyński and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-23 with Diffusion processes categories.
Diffusion Processes, Jump Processes, and Stochastic Differential Equations provides a compact exposition of the results explaining interrelations between diffusion stochastic processes, stochastic differential equations and the fractional infinitesimal operators. The draft of this book has been extensively classroom tested by the author at Case Western Reserve University in a course that enrolled seniors and graduate students majoring in mathematics, statistics, engineering, physics, chemistry, economics and mathematical finance. The last topic proved to be particularly popular among students looking for careers on Wall Street and in research organizations devoted to financial problems. Features Quickly and concisely builds from basic probability theory to advanced topics Suitable as a primary text for an advanced course in diffusion processes and stochastic differential equations Useful as supplementary reading across a range of topics.