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.


60J65 Brownian motion
60G17 Sample path properties
60J55 Local time and additive functionals
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