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In this paper, we consider an inverse problem for a general class of nonlinear stochastic differential equations on finite dimensional spaces whose generating operators (drift, diffusion and Jump kernel) are unknown. We introduce a class of function spaces with a suitable topology and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel). Also we present briefly an alternative approach giving the Hamilton-Jacobi-Bellman (HJB) equation and discuss the merits and demerits of the two methods. This paper is an extension of our previous studies on similar inverse problem for continuous diffusion. 

nonlinear stochastic systems, Lévy process, inverse problem, identification, existence of optimal drift-diffusion-jump triples, necessary conditions of optimality.