Integro-Differential Equations Generated by Stochastic Problems.

Melnikova, I. V.; Bovkun, V. A.; Alekseeva, U. A.

The connections between stochastic differential equations in which continuous and discontinuous random processes serve as sources of randomness and deterministic equations for the 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's formula), on the analysis of local infinitesimal characteristics of the process, and on the theory of semigroups of operators in combination with the generalized Fourier transform. This allows us to obtain direct and inverse integro-differential equations for various probabilistic characteristics.

STOCHASTIC differential equations; STOCHASTIC processes; RANDOM variables; FOURIER transforms; OPERATOR theory; INTEGRO-differential equations

Differential Equations, 2021, Vol 57, Issue 3, p379

0012-2661

Academic Journal

10.1134/S0012266121030101