ON PROBABILITY LAWS OF SOLUTIONS TO DIFFERENTIAL SYSTEMS DRIVEN BY A FRACTIONAL BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Baudoin, F.; Nualart, E.; Ouyang, C.; Tindel, S.
• 署名单位: Purdue University System; Purdue University; Pompeu Fabra University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Universite de Lorraine
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1028
• 发表日期: 2016
• 页码: 2554-2590
• 关键词: equations driven; rough paths; density; Integrability; calculus

摘要

This article investigates several properties related to densities of solutions (X-t)(t is an element of[0,1]) to differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/4. We first determine conditions for strict positivity of the density of X-t. Then we obtain some exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition. Finally, still in the elliptic case, we derive some bounds on the hitting probabilities of sets by fractional differential systems in terms of Newtonian capacities.