Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups - Mathematics > ProbabilityReport as inadecuate




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Abstract: We consider stochastic equations in Hilbert spaces with singular drift in theframework of Da Prato, R\-ockner, PTRF 2002. We prove a Harnack inequalityin the sense of Wang, PTRF 1997 for its transition semigroup and exploitits consequences. In particular, we prove regularizing and ultraboundednessproperties of the transition semigroup as well as that the correspondingKolmogorov operator has at most one infinitesimally invariant measure $\mu$satisfying some mild integrability conditions. Finally, we prove existence ofsuch a measure $\mu$ for non-continuous drifts.



Author: Giuseppe Da Prato, Michael Röckner, Feng-Yu Wang

Source: https://arxiv.org/



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