Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators / Andreas Eberle
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1718Langue : anglais.Éditeur : Berlin : Springer, 1999ISBN: 3540666281.ISSN: 1617-9692.Sujet MSC : 60J60, Probability theory and stochastic processes - Markov processes, Diffusion processes47D07, Operator theory - Groups and semigroups of linear operators, their generalizations and applications, Markov semigroups and applications to diffusion processes
60H10, Probability theory and stochastic processes - Stochastic analysis, Stochastic ordinary differential equations
31C25, Generalizations of potential theory, Dirichlet formsEn-ligne : Springerlink | Zentralblatt | MathScinet
The work under review is a very carefully written monograph on the uniqueness problem for sub-Markovian semigroups generated by singular diffusion operators in both finite- and infinite-dimensional state spaces. In fact, the discussion is not confined only to known results; the author contributes in the treatise (as earlier in a few papers) many new highly original results. In addition many illuminating examples (and counterexamples) are presented, too many to mention individually. The introduction provides clear motivation for the relevance of the problem from the mathematical point of view as well as from the point of view of some applications in mathematical physics (think of the problem of essential self-adjointness). ... (MathSciNet)
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