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Differential Equations in Banach Spaces Multiplicatively Perturbed by Random Noise

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Abstract

We consider the problem to find the moment functions of the solution of the Cauchy problem for a first-order linear inhomogeneous differential equation with random coefficients in a Banach space. The problem is reduced to the initial problem for a nonrandom differential equation with ordinary and variational derivatives. We obtain explicit expressions for the mathematical expectation and the second-order mixed moment functions for the solution of the equation.

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References

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Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    V. G. Zadorozhniy & M. A. Konovalova

Authors
  1. V. G. Zadorozhniy
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  2. M. A. Konovalova
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Corresponding author

Correspondence to V. G. Zadorozhniy.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 63, No. 4, Differential and Functional Differential Equations, 2017.

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Zadorozhniy, V.G., Konovalova, M.A. Differential Equations in Banach Spaces Multiplicatively Perturbed by Random Noise. J Math Sci 259, 817–832 (2021). https://doi.org/10.1007/s10958-021-05664-0

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  • DOI: https://doi.org/10.1007/s10958-021-05664-0

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