Regularising Flows and Singular Fractional SDEs with Superlinear Dissipation
Abstract
We study stochastic differential equations driven by the fractional Riemann-Liouville process with Hurst parameter H∈(0,1), whose drift is the sum of a possibly distributional vector field b and a smooth, one-sided Lipschitz, dissipative vector field F with coercivity of order k+1 and polynomially growing derivatives. If b ∈ 𝒞γ(ℝd;ℝd) for some γ<1 satisfying γ>max{1−1/(2H),2−1/H}, and if H+1/(k−1)>(1−γ)H/2, we construct a solution by smooth approximation and prove uniqueness in a class defined through local comparison with the flow generated by the dissipative drift. We also establish quantitative temporal regularity and stability estimates. The proof combines a conditional decomposition of fractional Brownian motion, Malliavin integration by parts, uniform non-degeneracy estimates for the regularising flow, and the stochastic sewing lemma.
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BibTeX
@misc{dareiotis2026regularising,
title = {{Regularising Flows and Singular Fractional SDEs with Superlinear Dissipation}},
author = {Konstantinos Dareiotis and El Mehdi Haress and Khoa Lê},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23113},
eprint = {2610.23113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23113},
}
RIS
TY - UNPB
TI - Regularising Flows and Singular Fractional SDEs with Superlinear Dissipation
AU - Konstantinos Dareiotis
AU - El Mehdi Haress
AU - Khoa Lê
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23113
UR - https://arxiv.org/abs/2610.23113
AB - We study stochastic differential equations driven by the fractional Riemann-Liouville process with Hurst parameter H∈(0,1), whose drift is the sum of a possibly distributional vector field b and a smooth, one-sided Lipschitz, dissipative vector field F with coercivity of order k+1 and polynomially growing derivatives. If b ∈ 𝒞^γ(ℝ^d;ℝ^d) for some γ<1 satisfying γ>max{1−1/(2H),2−1/H}, and if H+1/(k−1)>(1−γ)H/2, we construct a solution by smooth approximation and prove uniqueness in a class defined through local comparison with the flow generated by the dissipative drift. We also establish quantitative temporal regularity and stability estimates. The proof combines a conditional decomposition of fractional Brownian motion, Malliavin integration by parts, uniform non-degeneracy estimates for the regularising flow, and the stochastic sewing lemma.
ER -