Articlegreen2017

Integrability conditions for SDEs and semilinear SPDEs

17 citations0/0 files storedThe Annals of Probability

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Geometric Analysis and Curvature Flows

Abstract

By using the local dimension-free Harnack inequality established on incomplete Riemannian manifolds, integrability conditions on the coefficients are presented for SDEs to imply the nonexplosion of solutions as well as the existence, uniqueness and regularity estimates of invariant probability measures. These conditions include a class of drifts unbounded on compact domains such that the usual Lyapunov conditions cannot be verified. The main results are extended to second-order differential operators on Hilbert spaces and semilinear SPDEs.

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References

2004Strong solutions of stochastic equations with singular time dependent drift 2011Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients 2005Strong solutions of SDES with singular drift and Sobolev diffusion coefficients 2016Degenerate SDE with Hölder--Dini Drift and Non-Lipschitz Noise Coefficient 2015Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift 2017Strong existence and uniqueness for degenerate SDE with Hölder drift 2014Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term

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