Distribution dependent SDEs driven by additive fractional Brownian motion

被引：14

作者：

Galeati, Lucio ^{[1
]}

Harang, Fabian A. ^{[2
,3
]}

Mayorcas, Avi ^{[4
]}

机构：

[1] Univ Bonn, Inst Appl Math, Endenicher Allee 60, D-53115 Bonn, Germany

[2] Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway

[3] BI Norwegian Business Sch, Dept Econ, Nydalsveien 37, Oslo, Norway

[4] Univ Cambridge, DPMMS, CMS, Wilberforce Rd, Cambridge CB3 0WB, England

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2023年 / 185卷 / 1-2期

关键词：

Distribution dependent SDEs; Singular drifts; Regularization by noise; Fractional Brownian motion; MEAN-FIELD LIMIT; DIFFERENTIAL-EQUATIONS; REGULARIZATION; PROPAGATION; CHAOS;

D O I：

10.1007/s00440-022-01145-w

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：251 / 309

页数：59

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