Existence and pathwise uniqueness of solutions for stochastic differential equations with respect to martingales in the plane

In this paper we establish some new theorems on pathwise uniqueness of solutions to the stochastic differential equations of the form of X-z = Z((s,0)) + Z((0,t)) - Z((0,0)) + integral(Rz) a((xi),X-xi) dM(xi) + integral(Rz) b(xi,X-xi) dA(xi) for z =(s,t) is an element of R-+(2) with non-Lipschitz coefficients, were M = {M-z, z is an element of R-+(2)} is a continuous square integrable martingale and A = {A(z), z is an element of R-+(2)} is a continuous increasing process, Z is a continuous stochastic process on boundary partial derivative R-+(2) of R-+(2). We have proved existence theorem for the equation in Liang (1996a). (C) 1999 Elsevier Science B.V. All rights reserved.