A new approach to intersection local times of Brownian motion is given
, using additive functionals of a single Markov process and stochastic
calculus. New results include the Tanaka formula for the k-multiple p
oints of self-intersection local time and the joint Holder continuity
in all variables of renormalized self-intersection local time for k-mu
ltiple points, k greater-than-or-equal-to 4.