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Diffusions and Elliptic Operators : Probability and Its Applications - Richard F. Bass

Diffusions and Elliptic Operators

Probability and Its Applications

Hardcover

Published: 25th November 1997
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A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with stochastic 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.

Stochastic Differential Equations
Representations of Solutions
Regularity of Solutions
One Dimensional Diffusions
Nondivergence Form Operators]
Martingale Problems
Divergence Form Operators
The Malliavin Calculus
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387983158
ISBN-10: 0387983155
Series: Probability and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 232
Published: 25th November 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 2.54
Weight (kg): 1.18