Eberle, Andreas.
Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators [electronic resource] / by Andreas Eberle. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1999. - VIII, 268 p. online resource. - Lecture Notes in Mathematics, 1718 0075-8434 ; . - Lecture Notes in Mathematics, 1718 .
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.
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.
9783540480761
10.1007/BFb0103045 doi
Mathematics.
Differential equations, partial.
Potential theory (Mathematics).
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Partial Differential Equations.
Potential Theory.
QA273.A1-274.9 QA274-274.9
519.2
Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators [electronic resource] / by Andreas Eberle. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1999. - VIII, 268 p. online resource. - Lecture Notes in Mathematics, 1718 0075-8434 ; . - Lecture Notes in Mathematics, 1718 .
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.
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.
9783540480761
10.1007/BFb0103045 doi
Mathematics.
Differential equations, partial.
Potential theory (Mathematics).
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Partial Differential Equations.
Potential Theory.
QA273.A1-274.9 QA274-274.9
519.2