2019/06/29 by Xi Geng, Cheng Ouyang, Geng, Xi +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1907.00171
openalex publication_date 2019/06/29 · openalex created_date 2019/07/12 · openalex updated_date 2026/07/28
This article is concerned with stochastic differential equations driven by a d dimensional fractional Brownian motion with Hurst parameter H>1/4, 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.