Log-Harnack Inequality for Stochastic Differential Equations in Hilbert Spaces and its Consequences

By Michael Röckner, Feng-Yu Wang. 2009

84 citations recorded by the source corpus.

A logarithmic type Harnack inequality is established for the semigroup of solutions to a stochastic differential equation in Hilbert spaces with non-additive noise. As applications, the strong Feller property as well as the entropy-cost inequality for the semigroup are derived with respect to the corresponding distance (cost function).

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f5c66cf9402c15786c2b88d21fb468990a3bdb7a

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Citations in the corpus

Harnack inequalities for stochastic equations driven by Levy noise (2012, background): “1 Introduction Due to their broad range of applications in heat kernel estimates, functional inequalities, transportation-cost inequalities and properties of invariant measures, the dimension-free Harnack inequality with powers introduced in [14] and the log-Harnack inequality introduced in [9] have”
Semi Log-Concave Markov Diffusions (2013, background): “In addition to [22] for transportation inequalities, and [41, 46], one can also mention [14, 15] where similar ideas are used to study hyper-boundedness.”
Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift (2014, background): “(1) According to [17, 23], the key point in the proof of Theorem 1.”