Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift

Da Prato G, Flandoli F, Priola E, Röckner M (2013)
The Annals Of Probability 41(5): 3306-3344.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Da Prato, Giuseppe; Flandoli, F.; Priola, E.; Röckner, MichaelUniBi
Abstract / Bemerkung
We prove pathwise (hence strong) uniqueness of solutions to stochastic evolution equations in Hilbert spaces with merely measurable bounded drift and cylindrical Wiener noise, thus generalizing Veretennikov's fundamental result on R-d 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.
Stichworte
Pathwise uniqueness; stochastic PDEs; bounded measurable drift
Erscheinungsjahr
2013
Zeitschriftentitel
The Annals Of Probability
Band
41
Ausgabe
5
Seite(n)
3306-3344
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2636018

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Da Prato G, Flandoli F, Priola E, Röckner M. Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift. The Annals Of Probability. 2013;41(5):3306-3344.
Da Prato, G., Flandoli, F., Priola, E., & Röckner, M. (2013). Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift. The Annals Of Probability, 41(5), 3306-3344. doi:10.1214/12-AOP763
Da Prato, G., Flandoli, F., Priola, E., and Röckner, M. (2013). Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift. The Annals Of Probability 41, 3306-3344.
Da Prato, G., et al., 2013. Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift. The Annals Of Probability, 41(5), p 3306-3344.
G. Da Prato, et al., “Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift”, The Annals Of Probability, vol. 41, 2013, pp. 3306-3344.
Da Prato, G., Flandoli, F., Priola, E., Röckner, M.: Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift. The Annals Of Probability. 41, 3306-3344 (2013).
Da Prato, Giuseppe, Flandoli, F., Priola, E., and Röckner, Michael. “Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift”. The Annals Of Probability 41.5 (2013): 3306-3344.

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