CHAOS EXPANSION OF LOCAL TIME OF FRACTIONAL BROWNIAN MOTIONS

We find the chaos expansion of local time ? _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 ? _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 ? _T ^(H)(x,·)∈L ²(μ) for all H∈(0,1).