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.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 2, Dedicated to the memory of Professor N. D. Kopachevsky, 2021.
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Melnikova, I.V., Alekseeva, U.A. & Bovkun, V.A. Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform. J Math Sci 278, 115–138 (2024). https://doi.org/10.1007/s10958-024-06909-4
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DOI: https://doi.org/10.1007/s10958-024-06909-4