Diffusions and Elliptic Operators
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Book Overview
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.
Format:Paperback
Language:English
ISBN:1475771592
ISBN13:9781475771596
Release Date:July 2013
Publisher:Springer
Length:232 Pages
Weight:0.79 lbs.
Dimensions:0.5" x 6.1" x 9.2"
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