PRECISE LOCAL ESTIMATES FOR DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION: HYPOELLIPTIC CASE

• 成果类型: Article
• 署名作者: Geng, Xi; Ouyang, Cheng; Tindel, Samy
• 署名单位: University of Melbourne; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Purdue University System; Purdue University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1542
• 发表日期: 2022
• 页码: 649-687
• 关键词: stochastic-analysis; INEQUALITY; THEOREM

摘要

This article is concerned with stochastic differential equations driven by a d dimensional fractional Brownian motion with Hurst parameter H > 1/4 and understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform hypoellipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution. Our methodology relies heavily on the rough paths structure of the equation.