On the existence and uniqueness of solutions to stochastic differential equations of mixed Brownian and Poissonian sheet type

Let be a two-parameter semimartingale, where M is a continuous martingale, [Lambda] is the character of the Poisson point measure Y, N=Y-[Lambda], we prove that f(Xz) is expressible as such a sum once again via the partial differentiation formula, where f is a twice continuously differentiable function. Then, we prove a new theorem on the existence and uniqueness of solutions to the mixed Brownian and Poissonian sheet type stochastic differential equations with non-Lipschitz coefficients by applying the partial differentiation formula.