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A local time approach to the self-intersections of Brownian paths in space. (English) Zbl 0534.60070
Summary: We study the Brownian functional $$\alpha(x,B)=\iint_{B}\delta_ x(W_ t-W_ s)dsdt,$$ where $$W_ t$$ is a Brownian path in two or three dimensions. For B off the diagonal we identify $$\alpha$$ (x,B) with a local time, and establish the Hölder continuity of $$\alpha$$ (x,B) in both x and B.

##### MSC:
 60J65 Brownian motion 60G17 Sample path properties 60J55 Local time and additive functionals
##### Keywords:
self-intersections; polymers; local time; Hölder continuity
Full Text:
##### References:
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