Markov Processes and Differential Equations

Markov Processes and Differential Equations
Author :
Publisher : Birkhäuser
Total Pages : 155
Release :
ISBN-10 : 9783034891912
ISBN-13 : 3034891911
Rating : 4/5 (911 Downloads)

Book Synopsis Markov Processes and Differential Equations by : Mark I. Freidlin

Download or read book Markov Processes and Differential Equations written by Mark I. Freidlin and published by Birkhäuser. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations. Due to the close connection between the second order differential operators with a non-negative characteristic form on the one hand and Markov processes on the other, many problems in PDE's can be reformulated as problems for corresponding stochastic processes and vice versa. In the present book four classes of problems are considered: - the Dirichlet problem with a small parameter in higher derivatives for differential equations and systems - the averaging principle for stochastic processes and PDE's - homogenization in PDE's and in stochastic processes - wave front propagation for semilinear differential equations and systems. From the probabilistic point of view, the first two topics concern random perturbations of dynamical systems. The third topic, homog- enization, is a natural problem for stochastic processes as well as for PDE's. Wave fronts in semilinear PDE's are interesting examples of pattern formation in reaction-diffusion equations. The text presents new results in probability theory and their applica- tion to the above problems. Various examples help the reader to understand the effects. Prerequisites are knowledge in probability theory and in partial differential equations.


Markov Processes and Differential Equations Related Books

Markov Processes and Differential Equations
Language: en
Pages: 155
Authors: Mark I. Freidlin
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

GET EBOOK

Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations.
Markov Processes from K. Itô's Perspective (AM-155)
Language: en
Pages: 289
Authors: Daniel W. Stroock
Categories: Mathematics
Type: BOOK - Published: 2003-05-06 - Publisher: Princeton University Press

GET EBOOK

Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory o
Controlled Markov Processes and Viscosity Solutions
Language: en
Pages: 436
Authors: Wendell H. Fleming
Categories: Mathematics
Type: BOOK - Published: 2006-02-04 - Publisher: Springer Science & Business Media

GET EBOOK

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic program
Continuous Parameter Markov Processes and Stochastic Differential Equations
Language: en
Pages: 502
Authors: Rabi Bhattacharya
Categories: Mathematics
Type: BOOK - Published: 2023-11-16 - Publisher: Springer Nature

GET EBOOK

This graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developi
Stochastic Differential Equations and Applications
Language: en
Pages: 248
Authors: Avner Friedman
Categories: Mathematics
Type: BOOK - Published: 2014-06-20 - Publisher: Academic Press

GET EBOOK

Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume