Multiple Intersection Local Time of Planar Brownian Motion as a Particular Hida Distribution

Subspaces of the space of Hida distributions are quantified in which the multiple intersection local time of planar Brownian motion, renormalized by taking off the term of order zero in its chaos decomposition, lives. This is done by means of a new formula expressing the expectation of higher products of multiple Wiener–Ito-integrals by certain functions of the scalar products of their kernels.