A local time analysis of intersections of Brownian paths in the plane. (English) Zbl 0536.60046

Let \(W_ i(t)\), \(i=1,...,N\) be independent planar Brownian motions. The set of times \((t_ 1,...,t_ N) \in R^ N_+\) for which \(W_ 1(t_ 1)=W_ 2(t_ 2)=...=W_ N(t_ N)\) are studied by means of the local time of \(X(t)=(W_ 1(t_ 1)-W_ 2(t_ 2),...,W_{N-1}(t_{N-1})- W_ N(t_ N))\). The main result asserts that this local time is jointly continuous and gives local and global Hölder-type conditions for it in the time variable.
Reviewer: J.Cuzick


60G15 Gaussian processes
60G17 Sample path properties
60J65 Brownian motion
60G60 Random fields
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