Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Elliptic Case

Xi Geng (), Cheng Ouyang () and Samy Tindel ()
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Xi Geng: University of Melbourne
Cheng Ouyang: University of Illinois at Chicago
Samy Tindel: Purdue University

Journal of Theoretical Probability, 2023, vol. 36, issue 3, 1341-1367

Abstract: Abstract This article is concerned with stochastic differential equations driven by a d-dimensional fractional Brownian motion with Hurst parameter $$H>1/4$$ H > 1 / 4 , understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform ellipticity 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.

Keywords: Rough paths; Malliavin calculus; Fractional Brownian motion; Density function; 60H10; 60H07; 60G15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01208-7

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