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.
"Harnack inequalities for stochastic (functional) differential equations with non-Lipschitzian coefficients." Electron. J. Probab. 17 1 - 18, 2012. https://doi.org/10.1214/EJP.v17-2140