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July 2011 Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds
Feng-Yu Wang
Ann. Probab. 39(4): 1449-1467 (July 2011). DOI: 10.1214/10-AOP600

Abstract

By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of stochastic differential equations with multiplicative noise. These inequalities are applied to the study of heat kernel upper bound and contractivity properties of the semigroup. The main results are also extended to reflecting diffusion processes on Riemannian manifolds with nonconvex boundary.

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Feng-Yu Wang. "Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds." Ann. Probab. 39 (4) 1449 - 1467, July 2011. https://doi.org/10.1214/10-AOP600

Information

Published: July 2011
First available in Project Euclid: 5 August 2011

zbMATH: 1238.60069
MathSciNet: MR2857246
Digital Object Identifier: 10.1214/10-AOP600

Subjects:
Primary: 47G20 , 60H10

Keywords: Harnack inequality , Manifold , Neummann semigroup , Stochastic differential equation

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 4 • July 2011
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