Harnack Inequalities for Stochastic (Functional) Differential Equations   with Non-Lipschitzian Coefficients
  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. 
Jinghai Shao, Feng-Yu Wang, Chenggui Yuan
math.PR