Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups

By Giuseppe Da Prato, Michael Röckner, Feng-Yu Wang. 2008

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We consider stochastic equations in Hilbert spaces with singular drift in the framework of [Da Prato, R\"ockner, PTRF 2002]. We prove a Harnack inequality (in the sense of [Wang, PTRF 1997]) for its transition semigroup and exploit its consequences. In particular, we prove regularizing and ultraboundedness properties of the transition semigroup as well as that the corresponding Kolmogorov operator has at most one infinitesimally invariant measure $\mu$ (satisfying some mild integrability conditions). Finally, we prove existence of such a measure $\mu$ for non-continuous drifts.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/9a484ceefec3e65596c7b39fa816969cb9fa0516

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In Applied Mathematics

In Computational Theory and Mathematics

In Finance

Citations in the corpus

Log-Harnack Inequality for Stochastic Differential Equations in Hilbert Spaces and its Consequences (2009, methodology): “ inequalities for the associated Dirichlet form, the hyper-/super-/ultracontractivity properties of the semigroup, strong Feller property as well as estimates on the heat kernel of the semigroup (cf. [8, 13, 15, 6] and references therein). To establish this inequality for diﬀusions with curvature un”