Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators (Paperback)

Andreas Eberle

ISBN 10: 3540666281 / ISBN 13: 9783540666288

Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 1999

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Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9783540666288

Dati bibliografici

• Titolo: Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators (Paperback)
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
• Data di pubblicazione: 1999
• Lingua: Inglese
• ISBN 10: 3540666281
• ISBN 13: 9783540666288
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

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.

Contenuti

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.