Distribution dependent SDEs driven by fractional Brownian motion with singular coefficients
Peer reviewed, Journal article
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We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter H∈(0,1). We establish strong well-posedness under a variety of assumptions on the drift; these include the choice B(⋅,μ)=(f∗μ)(⋅)+g(⋅),f,g∈Bα∞,∞,α>1−12H, thus extending the results by Catellier and Gubinelli (Stochast Process Appl 126(8):2323–2366, 2016) 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.