Singular dissipative stochastic equations in Hilbert spaces

Existence of solutions to martingale problems corresponding to singular dissipative stochastic equations in Hilbert spaces are proved for any initial condition. The solutions for the single starting points form a conservative diffusion process whose transition semigroup is shown to be strong Feller....

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Bibliographic Details
Published in:Probability theory and related fields 2002-10, Vol.124 (2), p.261-303
Main Authors: DA PRATO, Giuseppe, RÖCKNER, Michael
Format: Article
Language:English
Subjects:
Diffusion
Dissipation
Exact sciences and technology
Hilbert space
Initial conditions
Martingales
Mathematical analysis
Mathematics
Operator theory
Partial differential equations
Probability
Probability and statistics
Probability theory
Probability theory and stochastic processes
Sciences and techniques of general use
Stochastic analysis
Stochasticity
Uniqueness
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Summary:Existence of solutions to martingale problems corresponding to singular dissipative stochastic equations in Hilbert spaces are proved for any initial condition. The solutions for the single starting points form a conservative diffusion process whose transition semigroup is shown to be strong Feller. Uniqueness in a generalized sense is proved also, and a number of applications is presented.
ISSN:0178-8051
1432-2064
DOI:10.1007/s004400200214