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.

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