Global Properties of Transition Probabilities of Singular Diffusions

We prove global Sobolev regularity and pointwise upper bounds for transition densities associated with second order differential operators in R^sup N^ with unbounded drift. As an application, we obtain sufficient conditions implying the differentiability of the associated transition semigroup on the...

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Bibliographic Details
Published in:Theory of probability and its applications 2010-01, Vol.54 (1), p.68-96
Main Authors: Metafune, G, Pallara, D, Rhandi, A
Format: Article
Language:English
Subjects:
Density
Differential equations
Diffusion
Drift
Mathematical analysis
Operators
Probability distribution
Regularity
Studies
Transition probabilities
Upper bounds
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Summary:We prove global Sobolev regularity and pointwise upper bounds for transition densities associated with second order differential operators in R^sup N^ with unbounded drift. As an application, we obtain sufficient conditions implying the differentiability of the associated transition semigroup on the space of bounded and continuous functions on R^sup N^. [PUBLICATION ABSTRACT]
ISSN:0040-585X
1095-7219
DOI:10.1137/s0040585x97984012