A note on Harnack and Transportation inequalities For Stochastic Differential Equations with reflections

Abstract: We establish transportation cost inequalities, with respect to the uniform and $L_2$-metric, on the path space of continuous functions, for laws of solutions of stochastic differential equations with reflections. We also consider the case of stochastic differential equations involving local times. Harnack inequalities for the associated semigroups are also established.