Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators

ISBN-13: 9783540666288 / Angielski / Miękka / 1999 / 268 str.

Andreas Eberle; A. Eberle

Opis

This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts.

Spis treści

Motivation and basic definitions: Uniqueness problems in various contexts.- L p uniqueness in finite dimensions.- Markov uniqueness.- Probabilistic aspects of L p and Markov uniqueness.- First steps in infinite dimensions.