Local times of stochastic differential equations driven by fractional Brownian motions

In this paper, we study the existence and (Hölder) 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 Hölder exponent (in t) of the local time is 1−H, where H is the Hurst parameter of the driving fractional Brownian motion.