Remarks on the intersection local time of fractional Brownian motions

Let BH and be two independent d-dimensional fractional Brownian motions with Hurst parameter H[set membership, variant](0,1). Assume that d>=2. In this paper we consider the so-called intersection local time where [delta] denotes the Dirac delta function. We prove the existence of the random variable in L2. As a related problem, we also discuss the necessary and sufficient conditions for to be smooth in the sense of Meyer-Watanabe. The condition says that it is smooth if and only if .Intersection local time Fractional Brownian motion Chaos expansion