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Existence of solutions of stochastic differential inclusions with standard and fractional Brownian motions

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Abstract

We prove the existence of weak and strong solutions of stochastic differential inclusions dX(t) ∈ F(t,X(t))dt + G W (t,X(t))dW(t) + G B (t,X(t))dB H(t), X ∈ R d, with standard and fractional Brownian motions, Borel measurable locally bounded multimappings F and G W , and a multimapping GB satisfying the local Hölder condition.

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Authors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    A. A. Levakov & M. M. Vas’kovskii

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  1. A. A. Levakov
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  2. M. M. Vas’kovskii
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Correspondence to A. A. Levakov.

Additional information

Original Russian Text © A.A. Levakov, M.M. Vas’kovskii, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 8, pp. 997–1003.

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Levakov, A.A., Vas’kovskii, M.M. Existence of solutions of stochastic differential inclusions with standard and fractional Brownian motions. Diff Equat 51, 991–997 (2015). https://doi.org/10.1134/S0012266115080030

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  • DOI: https://doi.org/10.1134/S0012266115080030

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