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Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform

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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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Authors and Affiliations

  1. Ural Federal University named after the First President of Russia B. Yeltsin, Ekaterinburg, Russia

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

Authors
  1. I. V. Melnikova
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  2. U. A. Alekseeva
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  3. V. A. Bovkun
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Correspondence to I. V. Melnikova.

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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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