Integrability conditions for SDEs and semilinear SPDEs | Zendy

FengYu Wang | Zendy

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Integrability conditions for SDEs and semilinear SPDEs

Author(s) -

FengYu Wang

Publication year - 2017

Publication title -

the annals of probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.184

H-Index - 98

eISSN - 2168-894X

pISSN - 0091-1798

DOI - 10.1214/16-aop1135

Subject(s) - mathematics , uniqueness , harnack's inequality , invariant (physics) , harnack's principle , stochastic differential equation , mathematical analysis , pure mathematics , hilbert space , dimension (graph theory) , stochastic partial differential equation , class (philosophy) , partial differential equation , mathematical physics , artificial intelligence , computer science

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 non-explosion 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 can not be verified. The main results are extended to second order differential operators on Hilbert spaces and semi-linear SPDEs.

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