Smoothness of Density for the Area Process of Fractional Brownian Motion

Abstract

We consider a process given by a two-dimensional fractional Brownian motion with Hurst parameter 1/3 < H < 1/2, along with an associated Lévy area, and prove the smoothness of a density for this process with respect to Lebesgue measure.

arXiv comment31 pages, 1 figure

References in corpus (2)

• Good rough path sequences and applications to anticipating stochastic calculus
• Hypoelliptic heat kernel inequalities on Lie groups

Cited by in corpus (5)

• Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths
• Doob--Meyer for rough paths
• Integrability of (non-)linear rough differential equations and integrals
• Upper bounds for the density of solutions of stochastic differential equations driven by fractional Brownian motions
• Smooth density for some nilpotent rough differential equations