Strong Solutions and Pathwise Control for Non-Linear Stochastic system with Poisson Jumps in n-Dimensional Space

The existence of a pathwise unique strong solution for the stochastic differential equation (S. D. E. ) with Poisson jumps in n-dimensional space without continuity assumption on drift coefficient, which even can be greater than linear growth, and without Lipsehitz condition on diffusion coefficients is obtained. Then the existence of a p athwise stochastic optimal Bang-Bang control for a very much non-linear systemwith Poisson jumps in w-dimensional space is derived. The result is also applied to obtain a maximum likelihood estimate (MLE) of parameter for some continuous,S. D. E. with non-Lipschitz cefficients in n-dimensional space.