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September 2017 Integrability conditions for SDEs and semilinear SPDEs
Feng-Yu Wang
Ann. Probab. 45(5): 3223-3265 (September 2017). DOI: 10.1214/16-AOP1135

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.

Citation

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Feng-Yu Wang. "Integrability conditions for SDEs and semilinear SPDEs." Ann. Probab. 45 (5) 3223 - 3265, September 2017. https://doi.org/10.1214/16-AOP1135

Information

Received: 1 October 2015; Revised: 1 June 2016; Published: September 2017
First available in Project Euclid: 23 September 2017

zbMATH: 06812204
MathSciNet: MR3706742
Digital Object Identifier: 10.1214/16-AOP1135

Subjects:
Primary: 60H15
Secondary: 60J45

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 5 • September 2017
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