PATH-BY-PATH REGULARISATION THROUGH MULTIPLICATIVE NOISE IN ROUGH, YOUNG, AND ORDINARY DIFFERENTIAL EQUATIONS

• 成果类型: Article
• 署名作者: Dareiotis, Konstantinos; Gerencser, Mate
• 署名单位: University of Leeds; Technische Universitat Wien
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1686
• 发表日期: 2024
• 页码: 1864-1902
• 关键词: theorem; driven; sdes

摘要

Differential equations perturbed by multiplicative fractional Brownian motions are considered. Depending on the value of the Hurst parameter H, the resulting equation is pathwise viewed as an ODE, YDE, or RDE. In all three regimes, we show regularisation by noise phenomena by proving the strongest kind of well-posedness with irregular drift: strong existence and path-by-path uniqueness. In the Young and smooth regime H > 1/2, the condition on the drift coefficient is optimal in the sense that it agrees with the one known for the additive case. In the rough regime H E (1/3, 1/2), we assume positive but arbitrarily small drift regularity for strong well-posedness, while for distributional drift we obtain weak existence.