... different from zero thanks to thepositivity of the integrand. Therefore, Hd ≥ 2 implies that AT= +∞.Now, we turn to the proof of sufficient condition. Suppose thatHd < 2. By symmetry, we haveAT= ... +12u2|ξ|2VarSH,1t−SH,1sfor all t, s ≥ 0.3. Existence of the intersection local timeThe aim of this section is to prove the existence of the intersectionlocal time of SHandSH, for an H =12and d ... the time interval [0, T ]. As we pointed out, this definition isonly formal. In order to give a rigorous meaning to T, we approximate the Dirac delta function by the heat kernelpε(x) = (2πε)−d2e−|x|22ε,...