Harnack Inequalities for Stochastic (Functional) Differential Equations with Non-Lipschitzian Coefficients

Abstract

By using coupling arguments, Harnack type inequalities are established for a class of stochastic (functional) differential equations with multiplicative noises and non-Lipschitzian coefficients. To construct the required couplings, two results on existence and uniqueness of solutions on an open domain are presented.

22 pages

References in corpus (3)

• Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
• Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds
• An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions

Cited by in corpus (4)

• Shift Harnack Inequality and Integration by Part Formula for Semilinear SPDE
• New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients
• Harnack inequalities for $1$-$d$ stochastic Klein-Gordon type equations
• Existence and uniqueness of global strong solutions for SDEs with jumps under a new sufficient condition