Local times of stochastic differential equations driven by fractional Brownian motions

TL;DR

This paper investigates the existence and regularity of local times for stochastic differential equations driven by fractional Brownian motions, revealing that in one dimension with H<1/2, the local time's H"older exponent is 1-H.

Contribution

It establishes the regularity properties of local times for SDEs driven by fractional Brownian motions, especially in the rough case H<1/2, which was previously less understood.

Findings

Local times exist for the studied SDEs.

H"older exponent of local time in one dimension is 1-H for H<1/2.

Provides regularity results in the rough case H<1/2.

Abstract

In this paper, we study the existence and (H\"older) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case H<1/2, the H\"older exponent (in t) of the local time is 1-H, where H is the Hurst parameter of the driving fractional Brownian motion.