Diffusions and Elliptic Operators / Edition 1

Diffusions and Elliptic Operators / Edition 1

by Richard F. Bass
     
 

ISBN-10: 0387983155

ISBN-13: 9780387983158

Pub. Date: 12/01/1997

Publisher: Springer New York

A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with shastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions. The author

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Overview

A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with shastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions. The author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators, as well as Martingale problems and the Malliavin calculus. While serving as a textbook for a graduate course on diffusion theory with applications to PDE, this will also be a valuable reference to researchers in probability who are interested in PDE, as well as for analysts interested in probabilistic methods.

Product Details

ISBN-13:
9780387983158
Publisher:
Springer New York
Publication date:
12/01/1997
Series:
Probability and Its Applications Series
Edition description:
1998
Pages:
252
Product dimensions:
6.14(w) x 9.21(h) x 0.03(d)

Table of Contents

Shastic Differential Equations.- Representations of Solutions.- Regularity of Solutions.- One Dimensional Diffusions.- Nondivergence Form Operators.- Martingale Problems.- Divergence Form Operators.- The Malliavin Calculus.

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