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Weak solutions to stochastic differential equations driven by fractional brownian motion

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Abstract

Existence of a weak solution to the n-dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter H ∈ (0, 1) \ {1/2} is shown for a time-dependent but state-independent diffusion and a drift that may by split into a regular part and a singular one which, however, satisfies the hypotheses of the Girsanov Theorem. In particular, a stochastic nonlinear oscillator driven by a fractional noise is considered.

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Authors and Affiliations

  1. Institute of Information Theory and Automation of the ASCR, Pod Vodárenskou věži 4, 182 08, Prague 8, Czech Republic

    J. Šnupárková

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  1. J. Šnupárková
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Correspondence to J. Šnupárková.

Additional information

This work was partially supported by the GAČR grant no. 201/07/0237.

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Šnupárková, J. Weak solutions to stochastic differential equations driven by fractional brownian motion. Czech Math J 59, 879–907 (2009). https://doi.org/10.1007/s10587-009-0062-y

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  • DOI: https://doi.org/10.1007/s10587-009-0062-y

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