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

Geman, Donald; Horowitz, Joseph; Rosen, Jay

Ann. Probab. 12, 86-107 (1984).

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