Title: Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform.
Authors: Melnikova, I. V.; Alekseeva, U. A.; Bovkun, V. A.
Abstract: The work is devoted to integro-differential equations related to stochastic processes. We study the relationship between differential equations with random perturbations — stochastic differential equations (SDEs) — and deterministic equations for the probability characteristics of processes determined by random perturbations. The resulting deterministic pseudodifferential equations are investigated by semigroup methods and Fourier transform methods.
Subjects: STOCHASTIC processes; STOCHASTIC differential equations; DIFFERENTIAL equations; EQUATIONS; SEPARATION of variables
Publication: Journal of Mathematical Sciences, 2024, Vol 278, Issue 1, p115
ISSN: 1072-3374
Publication type: Academic Journal
DOI: 10.1007/s10958-024-06909-4

Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform.

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