Large deviation principle for fractional Brownian motion with respect to capacity

TL;DR

This paper establishes a large deviation principle for fractional Brownian motion with Hurst parameter at least 1/2, viewed as a Wiener functional, with respect to capacity on classical Wiener space.

Contribution

It proves the quasi-sure definition of fractional Brownian motion and derives the LDP with respect to capacity in the Malliavin calculus framework.

Findings

Fractional Brownian motion is quasi-surely defined on Wiener space.

LDP is established for fBM with respect to (p,r)-capacity.

Results extend large deviation theory to fractional Brownian motion in a new capacity setting.

Abstract

We show that fractional Brownian motion(fBM) defined via Volterra integral representation with Hurst parameter $H\geq\frac{1}{2}$ is a quasi-surely defined Wiener functional on classical Wiener space,and we establish the large deviation principle(LDP) for such fBM with respect to $(p,r)$-capacity on classical Wiener space in Malliavin's sense.