On the solvability of the main inverse problem of stochastic differential systems

Abstract

Using the quasi-inversion method we obtain necessary and sufficient conditions for the solvability of the main (according to Galiullin’s classification) inverse problem in the class of first-order Itˆo stochastic differential systems with random perturbations from the class of processes with independent increments, with diffusion degenerate in a part of variables and with given properties, depending on a part of variables.