STRONG UNIQUENESS FOR STOCHASTIC EVOLUTION EQUATIONS IN HILBERT SPACES PERTURBED BY A BOUNDED MEASURABLE DRIFT
We prove pathwise (hence strong) uniqueness of solutions to stochastic evolution equations in Hubert spaces with merely measurable bounded drift and cylindrical Wiener noise, thus generalizing Veretennikov's fundamental result on ℝd to infinite dimensions. Because Sobolev regularity results imp...
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| Veröffentlicht in: | The Annals of probability 2013-09, Vol.41 (5), p.3306-3344 |
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| container_issue | 5 |
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| container_title | The Annals of probability |
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| creator | Da Prato, G. Flandoli, F. Priola, E. Röckner, M. |
| description | We prove pathwise (hence strong) uniqueness of solutions to stochastic evolution equations in Hubert spaces with merely measurable bounded drift and cylindrical Wiener noise, thus generalizing Veretennikov's fundamental result on ℝd to infinite dimensions. Because Sobolev regularity results implying continuity or smoothness of functions do not hold on infinite-dimensional spaces, we employ methods and results developed in the study of Malliavin-Sobolev spaces in infinite dimensions. The price we pay is that we can prove uniqueness for a large class, but not for every initial distribution. Such restriction, however, is common in infinite dimensions. |
| doi_str_mv | 10.1214/12-aop763 |
| format | Article |
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Because Sobolev regularity results implying continuity or smoothness of functions do not hold on infinite-dimensional spaces, we employ methods and results developed in the study of Malliavin-Sobolev spaces in infinite dimensions. The price we pay is that we can prove uniqueness for a large class, but not for every initial distribution. 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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 35R60 60H15 Approximation bounded measurable drift Brownian motion Determinism Dimensional analysis Evolution equations Geometry Hilbert space Hilbert spaces Martingales Mathematics Pathwise uniqueness Probabilities Probability distribution Semigroups Stochastic models stochastic PDEs Studies Topology Uniqueness |
| title | STRONG UNIQUENESS FOR STOCHASTIC EVOLUTION EQUATIONS IN HILBERT SPACES PERTURBED BY A BOUNDED MEASURABLE DRIFT |
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