Singular dissipative stochastic equations in Hilbert spaces

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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Veröffentlicht in:Probability theory and related fields 2002-10, Vol.124 (2), p.261-303
Hauptverfasser: DA PRATO, Giuseppe, RÖCKNER, Michael
Format: Artikel
Sprache:eng
Schlagworte:
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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Beschreibung
Zusammenfassung: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