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Mathematics - Probability Theory and Stochastic Processes | Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators

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

Series: Lecture Notes in Mathematics, Vol. 1718

Eberle, Andreas

1999, VIII, 268 p.

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  • About this book

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.

Content Level » Research

Keywords » Differential operator - differential equation - diffusion process - essentially self-adjoint - generator - partial differential equation - semigroup - uniqueness

Related subjects » Algebra - Analysis - Dynamical Systems & Differential Equations - Probability Theory and Stochastic Processes

Table of contents 

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.

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