Diffusions And Eliptic Operators - Bass Richard

Descripción

LIBRERÍA LEA+

This book discusses the interplay of diffusion processes and partial differential equations (PDEs) with an emphasis on probabilistic methods in PDEs. It begins with an emphasis on probabilistic methods ins PDEs. It beginds with stochastic differential equations, the probabilistic machinery needed to study PDEs. After spending hree chapters on probabilistic representations of solutions for PDEs, regularity of solutions, and one-dimensional diffusions, the author discusses in depth two main types of second-order linear differential operators: nondivergence operators and divergence operators, including such topics as the Harnack inequiality of Krylov-Safonov for nondivergence operators. Martingale problems and the Malliavin calculus are presented in two other chapters.

This book can be used as a tectbook for graduate course on diffusion theory with applications to PDEs. It will also be a valuable reference to researchers in probability who are interested in PDEs as well as to analyst who are interested in probabilistic methods

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