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 is an element of (0, 1) at a point x is an element of R-d. As an application we show that when H(0)d < 1 then l(T)((H))(x, (.)) is an element of L-2(mu). Here mu 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, (.)) is an element of L-2(mu) for all H is an element of (0, 1).