Distribution dependent SDEs driven by additive fractional Brownian motion

• 成果类型: Article
• 署名作者: Galeati, Lucio; Harang, Fabian A.; Mayorcas, Avi
• 署名单位: University of Bonn; University of Oslo; BI Norwegian Business School; University of Cambridge
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01145-w
• 发表日期: 2023
• 页码: 251-309
• 关键词: mean-field limit; differential-equations; regularization; propagation; chaos

摘要

We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter H is an element of (0, 1). We establish strong well-posedness under a variety of assumptions on the drift; these include the choice B(., mu) = (f * mu)(.) + g(.), f, g is an element of B-infinity,infinity(alpha), alpha > 1 - 1/2H, 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.