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arXiv · 2105.14063

Distribution dependent SDEs driven by additive fractional Brownian motion

Lucio Galeati·Fabian A. Harang·Avi Mayorcas
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Abstract

We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $H\in (0,1)$. We establish strong well-posedness under a variety of assumptions on the drift; these include the choice $$B(\cdot,\mu) = f\ast\mu(\cdot) + g(\cdot),\quad f,g\in B^\alpha_{\infty,\infty}, \quad \alpha>1-1/2H,$$ thus extending the results by Catellier and Gubinelli [9] to the distribution dependent case. The proofs rely on some novel stability estimates for singular SDEs driven by fractional Brownian motion and the use of Wasserstein distances.

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Lucio Galeati, Fabian A. Harang, Avi Mayorcas. 2021-05-28. Distribution dependent SDEs driven by additive fractional Brownian motion. https://arxiv.org/abs/2105.14063

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