Annals of Probability

Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds

Feng-Yu Wang

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 39, Number 4 (2011), 1449-1467.

Dates
First available in Project Euclid: 5 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aop/1312555804

Digital Object Identifier
doi:10.1214/10-AOP600

Mathematical Reviews number (MathSciNet)
MR2857246

Zentralblatt MATH identifier
1238.60069

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 47G20: Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx]

Keywords
Harnack inequality stochastic differential equation Neummann semigroup manifold

Citation

Wang, Feng-Yu. Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds. Ann. Probab. 39 (2011), no. 4, 1449--1467. doi:10.1214/10-AOP600. https://projecteuclid.org/euclid.aop/1312555804


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