Distribution dependent SDEs driven by additive fractional Brownian motion

Lucio Galeati, Fabian A. Harang, Avi Mayorcas

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)

Abstract

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∈B∞,∞α,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.

Original languageEnglish
Pages (from-to)251-309
Number of pages59
JournalProbability Theory and Related Fields
Volume185
Issue number1-2
Early online date20 May 2022
DOIs
Publication statusPublished - 1 Feb 2023

Bibliographical note

Funding Information:
FH gratefully acknowledges financial support from the STORM Project 274410, funded by the Research Council of Norway. LG is funded by the DFG under Germany’s Excellence Strategy - GZ 2047/1, Project-id 390685813.

Keywords

  • Distribution dependent SDEs
  • Fractional Brownian motion
  • Regularization by noise
  • Singular drifts

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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