Unique strong solutions of Levy processes driven stochastic differential   equations with discontinuous coefficients
  We establish the existence and uniqueness for a one-dimensional stochastic differential equation driven by a Brownian motion and a pure jump {\levy} process. It is shown that under fairly general conditions on the coefficients, pathwise uniqueness holds based on the methods of weak uniqueness and local time technique. 
Jie Xiong, Jiayu Zheng and Xiaowen Zhou
math.PR