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Diffusion Processes, Jump Processes, and Stochastic Differential Equations

2021-11-23 Diffusion processes
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Release : 2021-11-23
Genre : Diffusion processes
Kind : eBook
Book Rating : 678/5 ( reviews)

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Book Synopsis Diffusion Processes, Jump Processes, and Stochastic Differential Equations by : Wojbor Andrzej Woyczyński

Download or read book Diffusion Processes, Jump Processes, and Stochastic Differential Equations written by Wojbor Andrzej Woyczyński. This book was released on 2021-11-23. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Analysis and Diffusion Processes

2014-01-09 Mathematics
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Release : 2014-01-09
Genre : Mathematics
Kind : eBook
Book Rating : 529/5 ( reviews)

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Book Synopsis Stochastic Analysis and Diffusion Processes by : Gopinath Kallianpur

Download or read book Stochastic Analysis and Diffusion Processes written by Gopinath Kallianpur. This book was released on 2014-01-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Differential Equations and Diffusion Processes

2011-08-18 Mathematics
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Release : 2011-08-18
Genre : Mathematics
Kind : eBook
Book Rating : 12X/5 ( reviews)

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Book Synopsis Stochastic Differential Equations and Diffusion Processes by : S. Watanabe

Download or read book Stochastic Differential Equations and Diffusion Processes written by S. Watanabe. This book was released on 2011-08-18. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Differential Equations and Diffusion Processes

Stochastic Differential Equations and Diffusion Processes

1981
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Release : 1981
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Stochastic Differential Equations and Diffusion Processes by : Nobuyuki Ikeda

Download or read book Stochastic Differential Equations and Diffusion Processes written by Nobuyuki Ikeda. This book was released on 1981. 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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