Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term

Da Prato G, Flandoli F, Priola E, Röckner M (2015)
Journal of Theoretical Probability 28(4): 1571-1600.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Da Prato, Giuseppe; Flandoli, F.; Priola, E.; Röckner, MichaelUniBi
Abstract / Bemerkung
We consider stochastic evolution equations in Hilbert spaces with merely measurable and locally bounded drift term and cylindrical Wiener noise. We prove pathwise (hence strong) uniqueness in the class of global solutions. This paper extends our previous paper (Da Prato et al. in Ann Probab 41:3306-3344, 2013) which generalized Veretennikov's fundamental result to infinite dimensions assuming boundedness of the drift term. As in Da Prato et al. (Ann Probab 41:3306-3344, 2013), pathwise uniqueness holds for a large class, but not for every initial condition. We also include an application of our result to prove existence of strong solutions when the drift is assumed only to be measurable and bounded and grow more than linearly.
Stichworte
Pathwise uniqueness
Erscheinungsjahr
2015
Zeitschriftentitel
Journal of Theoretical Probability
Band
28
Ausgabe
4
Seite(n)
1571-1600
ISSN
0894-9840
eISSN
1572-9230
Page URI
https://pub.uni-bielefeld.de/record/2901026

Zitieren

Da Prato G, Flandoli F, Priola E, Röckner M. Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term. Journal of Theoretical Probability. 2015;28(4):1571-1600.
Da Prato, G., Flandoli, F., Priola, E., & Röckner, M. (2015). Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term. Journal of Theoretical Probability, 28(4), 1571-1600. doi:10.1007/s10959-014-0545-0
Da Prato, G., Flandoli, F., Priola, E., and Röckner, M. (2015). Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term. Journal of Theoretical Probability 28, 1571-1600.
Da Prato, G., et al., 2015. Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term. Journal of Theoretical Probability, 28(4), p 1571-1600.
G. Da Prato, et al., “Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term”, Journal of Theoretical Probability, vol. 28, 2015, pp. 1571-1600.
Da Prato, G., Flandoli, F., Priola, E., Röckner, M.: Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term. Journal of Theoretical Probability. 28, 1571-1600 (2015).
Da Prato, Giuseppe, Flandoli, F., Priola, E., and Röckner, Michael. “Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term”. Journal of Theoretical Probability 28.4 (2015): 1571-1600.

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