Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term

G. Prato (), F. Flandoli (), E. Priola () and M. Röckner ()
Additional contact information
G. Prato: Scuola Normale Superiore
F. Flandoli: Università di Pisa
E. Priola: Università di Torino
M. Röckner: Bielefeld University

Journal of Theoretical Probability, 2015, vol. 28, issue 4, 1571-1600

Abstract: Abstract We consider stochastic evolution equations in Hilbert spaces with merely measurable and locally bounded drift term $$B$$ B 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 $$B$$ B is assumed only to be measurable and bounded and grow more than linearly.

Keywords: Pathwise uniqueness; Stochastic PDEs; Locally bounded measurable drift term; Strong mild solutions; 35R60; 60H15 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10959-014-0545-0

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