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Author: H. Kunita
Publisher:
ISBN:
Category : Flows (Differentiable dynamical systems).
Languages : en
Pages : 144
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Book Description
Author: H. Kunita
Publisher:
ISBN:
Category : Flows (Differentiable dynamical systems).
Languages : en
Pages : 144
Get Book Here
Book Description
Author: Hiroshi Kunita
Publisher: Cambridge University Press
ISBN: 9780521599252
Category : Mathematics
Languages : en
Pages : 364
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Book Description
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.
Author: Fabrice Baudoin
Publisher: World Scientific
ISBN: 1860944817
Category : Mathematics
Languages : en
Pages : 152
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Book Description
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.
Author: Hiroshi Kunita
Publisher: Springer
ISBN: 9811338019
Category : Mathematics
Languages : en
Pages : 366
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Book Description
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.
Author: V. Wihstutz
Publisher: Springer Science & Business Media
ISBN: 1461203899
Category : Mathematics
Languages : en
Pages : 344
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Book Description
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.
Author: H. Kunita
Publisher: Springer
ISBN: 9783540177753
Category : Science
Languages : en
Pages : 121
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Book Description
These are the notes of a lecture course given by the author at the T.I.F.R. Centre, Bangalore in late 1985. The contents are divided into three chapters concluding with an extensive bibliography. Chapters 1 and 2 deal with basic properties of stochastic flows and especially of Brownian flows and their relations with local characteristics and stochastic differential equations. An appendix on the generalized Ito#^ formula, Stratonovich integral and Stratonovich stochastic differential equations has been added to Chapter 2. By the way of applications of the foregoing, limit theorems for stochastic flows, along with a unifying general limit theorem, are then presented in Chapter 3 including: - Approximation theorems for stochastic differential equations and stochastic flows, due to Bismut, Ikeda-Watanabe, Malliavin, Dowell etc. - Limit theorems for driving processes, due to Papanicolaou-Stroock-Varadhan, and - Limit theorems for stochastic differential equations, due to Khasminkii, Papanicolaou-Kohler, Kesten-Papanicolaou etc.
Author: Rene Carmona
Publisher: SIAM
ISBN: 1611974240
Category : Mathematics
Languages : en
Pages : 263
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Book Description
The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.
Author: Daniel W. Stroock
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Author: Bernt Oksendal
Publisher: Springer Science & Business Media
ISBN: 3662130505
Category : Mathematics
Languages : en
Pages : 218
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Book Description
These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.
Author: Grigorios A. Pavliotis
Publisher: Springer
ISBN: 1493913239
Category : Mathematics
Languages : en
Pages : 345
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Book Description
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
