Integral representation of renormalized self-intersection local times

Abstract

In this paper we apply Clark-Ocone formula to deduce an explicit integral representation for the renormalized self-intersection local time of the $d$% -dimensional fractional Brownian motion with Hurst parameter $H\in (0,1)$. As a consequence, we derive the existence of some exponential moments for this random variable.

References in corpus (2)

• Renormalized self-intersection local time for fractional Brownian motion
• Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm