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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The authors would like to thank the referees for their useful remarks and suggestions.
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M. Röckner’s research was supported by the DFG through IRTG 1132 and CRC 701 and the I. Newton Institute, Cambridge, UK.
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Da Prato, G., Flandoli, F., Priola, E. et al. Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term. J Theor Probab 28, 1571–1600 (2015). https://doi.org/10.1007/s10959-014-0545-0
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DOI: https://doi.org/10.1007/s10959-014-0545-0