Integro-Differential Equations Generated by Stochastic Problems

Abstract

Abstract: The connections between stochastic differential equations in which continuous anddiscontinuous random processes serve as sources of randomness and deterministic equations forthe probabilistic characteristics of solutions of these stochastic equations are studied. In the study,we use various approaches based on the stochastic change of variables formula (Itô’sformula), on the analysis of local infinitesimal characteristics of the process, and on the theory ofsemigroups of operators in combination with the generalized Fourier transform. This allows us toobtain direct and inverse integro-differential equations for various probabilistic characteristics. © 2021, Pleiades Publishing, Ltd.