Diffusion Processes And Stochastic Calculus

Author : N. Ikeda,S. Watanabe
Publisher : Elsevier
Page : 572 pages
File Size : 50,7 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483296159

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Stochastic Differential Equations and Diffusion Processes by N. Ikeda,S. Watanabe Pdf

Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,5 Mb
Release : 2014
Category : Electronic
ISBN : 3037196335

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Diffusion Processes and Stochastic Calculus by Anonim Pdf

Author : Gopinath Kallianpur,P Sundar
Publisher : OUP Oxford
Page : 368 pages
File Size : 47,8 Mb
Release : 2014-01-09
Category : Mathematics
ISBN : 9780191004520

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Stochastic Analysis and Diffusion Processes by Gopinath Kallianpur,P Sundar Pdf

Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.

Author : Fabrice Baudoin
Publisher : Erich Schmidt Verlag GmbH & Co. KG
Page : 292 pages
File Size : 53,5 Mb
Release : 2014
Category : Calculus
ISBN : 3037191333

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Diffusion Processes and Stochastic Calculus by Fabrice Baudoin Pdf

The main purpose of the book is to present, at a graduate level and in a self-contained way, the most important aspects of the theory of continuous stochastic processes in continuous time and to introduce some of its ramifications such as the theory of semigroups, the Malliavin calculus, and the Lyons' rough paths. This book is intended for students, or even researchers, who wish to learn the basics in a concise but complete and rigorous manner. Several exercises are distributed throughout the text to test the understanding of the reader and each chapter ends with bibliographic comments aimed at those interested in exploring the materials further. Stochastic calculus was developed in the 1950s and the range of its applications is huge and still growing today. Besides being a fundamental component of modern probability theory, domains of applications include but are not limited to: mathematical finance, biology, physics, and engineering sciences. The first part of the text is devoted to the general theory of stochastic processes. The author focuses on the existence and regularity results for processes and on the theory of martingales. This allows him to introduce the Brownian motion quickly and study its most fundamental properties. The second part deals with the study of Markov processes, in particular, diffusions. The author's goal is to stress the connections between these processes and the theory of evolution semigroups. The third part deals with stochastic integrals, stochastic differential equations and Malliavin calculus. In the fourth and final part, the author presents an introduction to the very new theory of rough paths by Terry Lyons.

Author : Kiyosi Itô,Henry P. Jr. McKean
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642620256

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Diffusion Processes and their Sample Paths by Kiyosi Itô,Henry P. Jr. McKean Pdf

Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 345 pages
File Size : 46,9 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781493913237

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Stochastic Processes and Applications by Grigorios A. Pavliotis Pdf

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.

Author : Wojbor A. Woyczyński
Publisher : CRC Press
Page : 138 pages
File Size : 49,5 Mb
Release : 2022-03-09
Category : Mathematics
ISBN : 9781000475357

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Diffusion Processes, Jump Processes, and Stochastic Differential Equations by Wojbor A. Woyczyński Pdf

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.

Author : Debasish Roy,G. Visweswara Rao,Gorti G.
Publisher : Cambridge University Press
Page : 749 pages
File Size : 43,7 Mb
Release : 2017-05-04
Category : Mathematics
ISBN : 9781107182646

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Stochastic Dynamics, Filtering and Optimization by Debasish Roy,G. Visweswara Rao,Gorti G. Pdf

This book introduces essential concepts in stochastic processes that interface seamlessly with applications of interest in science and engineering.

Author : Klebaner Fima C
Publisher : World Scientific Publishing Company
Page : 452 pages
File Size : 52,5 Mb
Release : 2012-03-21
Category : Mathematics
ISBN : 9781911298670

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Introduction To Stochastic Calculus With Applications (3rd Edition) by Klebaner Fima C Pdf

This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. It is also suitable for researchers to gain working knowledge of the subject. It contains many solved examples and exercises making it suitable for self study.In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. The book covers models in mathematical finance, biology and engineering. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises./a

Author : David Applebaum
Publisher : Cambridge University Press
Page : 440 pages
File Size : 47,6 Mb
Release : 2004-07-05
Category : Mathematics
ISBN : 0521832632

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Lévy Processes and Stochastic Calculus by David Applebaum Pdf

Publisher Description

Author : V. Wihstutz,M.A. Pinsky
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203896

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Diffusion Processes and Related Problems in Analysis, Volume II by V. Wihstutz,M.A. Pinsky Pdf

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 : Daniel W. Stroock,S.R.S. Varadhan
Publisher : Springer
Page : 338 pages
File Size : 47,9 Mb
Release : 2007-02-03
Category : Mathematics
ISBN : 9783540289999

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Multidimensional Diffusion Processes by Daniel W. Stroock,S.R.S. Varadhan Pdf

From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik

Author : Nobuyuki Ikeda,Shinzo Watanabe
Publisher : North Holland
Page : 555 pages
File Size : 40,9 Mb
Release : 1989
Category : Diffusion processes
ISBN : 4062032317

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Stochastic Differential Equations and Diffusion Processes by Nobuyuki Ikeda,Shinzo Watanabe Pdf

Author : Hiroshi Kunita
Publisher : Springer
Page : 352 pages
File Size : 47,8 Mb
Release : 2019-03-26
Category : Mathematics
ISBN : 9789811338014

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Stochastic Flows and Jump-Diffusions by Hiroshi Kunita Pdf

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 : Feng-Yu Wang
Publisher : World Scientific
Page : 392 pages
File Size : 49,5 Mb
Release : 2014
Category : Mathematics
ISBN : 9789814452656

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Analysis for Diffusion Processes on Riemannian Manifolds by Feng-Yu Wang Pdf

Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.