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

Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term

Da Prato, G.;Flandoli, F.;
2015

Abstract

We consider stochastic evolution equations in Hilbert spaces with merely measurable and locally bounded drift term 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 is assumed only to be measurable and bounded and grow more than linearly.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/69150
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