Equations related to stochastic processes: semigroup approach and Fourier transform

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

Contemporary Mathematics. Fundamental Directions, Dedicated to the memory of Professor N. D. Kopachevsky, Tome 67 (2021) no. 2, pp. 324-348.

Résumé

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 probabilistic characteristics of processes determined by random perturbations. The resulting deterministic pseudodifferential equations are investigated by semigroup methods and Fourier transform methods.

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