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Stochastic Differential Equations and Diffusion Processes

2014-06-28 Mathematics
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Release : 2014-06-28
Genre : Mathematics
Kind : eBook
Book Rating : 156/5 ( reviews)

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Book Synopsis Stochastic Differential Equations and Diffusion Processes by : N. Ikeda

Download or read book Stochastic Differential Equations and Diffusion Processes written by N. Ikeda. This book was released on 2014-06-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Diffusion Processes, Jump Processes, and Stochastic Differential Equations

2022-03-09 Mathematics
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Release : 2022-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 352/5 ( reviews)

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

Download or read book Diffusion Processes, Jump Processes, and Stochastic Differential Equations written by Wojbor A. Woyczyński. This book was released on 2022-03-09. 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 Processes and Applications

2014-11-19 Mathematics
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Release : 2014-11-19
Genre : Mathematics
Kind : eBook
Book Rating : 239/5 ( reviews)

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Book Synopsis Stochastic Processes and Applications by : Grigorios A. Pavliotis

Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis. This book was released on 2014-11-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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:

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.

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