CHAOS EXPANSION OF LOCAL TIME OF FRACTIONAL BROWNIAN MOTIONS

Abstract

We find the chaos expansion of local time ℓ T (H)(x,·) of fractional Brownian motion with Hurst coefficient H∈(0,1) at a point x∈R d . As an application we show that when H 0 d<1 then ℓ T (H)(x,·)∈L 2(μ). Here μ denotes the probability law of B (H) and H 0=max{H 1,…,H d }. In particular, we show that when d=1 then ℓ T (H)(x,·)∈L 2(μ) for all H∈(0,1).

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