INVERSE PROBLEM FOR STOCHASTIC DIFFERENTIAL EQUATIONS ON HILBERT SPACES DRIVEN BY LÉVY PROCESSES

Abstract

In this paper we consider inverse problem for a general class of nonlinear stochastic dierential equations on Hilbert spaces whose generating operators (drift, diusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces 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, diusion and jump kernel).