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Stability of Linear Stochastic Differential Equations of Mixed Type with Fractional Brownian Motions

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Abstract

We obtain sufficient as well as necessary and sufficient conditions for linear one-dimensional homogeneous stochastic differential equations with independent standard and fractional Brownian motions to possess some types of stability.

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ACKNOWLEDGMENTS

The author is grateful to M.M. Vas’kovskii for the proposed direction of research and for the attention to the work.

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  1. Belarusian State University, Minsk, 220030, Belarus

    I. V. Kachan

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  1. I. V. Kachan
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Correspondence to I. V. Kachan.

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Translated by V. Potapchouck

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Kachan, I.V. Stability of Linear Stochastic Differential Equations of Mixed Type with Fractional Brownian Motions. Diff Equat 57, 570–586 (2021). https://doi.org/10.1134/S0012266121050025

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