Tanaka's formula for multiple intersections of planar Brownian motion (Q1088302)

For any integer \(n\geq 1\), a planar Brownian motion W has n-multiple points, i.e. points z such that \(W_{t_ 1}=W_{t_ 2}=...=W_{t_ n}\) for distinct \(t_ 1,...,t_ n\). The local time of n-fold intersections is defined to be the local time at 0 of the random field \[ (t_ 1,...,t_ n)\to (W_{t_ 1}-W_{t_ 2},...,W_{t_{n-1}}- W_{t_ n}). \] The main result of the present paper is a Tanaka-like formula which relates the local times of n and \(n+1\)-fold intersections. The author also gives a simplified proof of the joint continuity of the local times of the above-mentioned random field.