## 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

### MSC:

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

### Keywords:

multiple points; planar Brownian motions; local time
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