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A local time approach to the self-intersections of Brownian paths in space

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Abstract

We study the Brownian functional

$$\alpha (x,B) = \int\limits_B {\int {\delta _x (W_t - W_s )dsdt} } $$

whereW t is a Brownian path in two or three dimensions. ForB off the diagonal we identify α(x, B) with a local time, and establish the Hölder continuity of α(x, B) in bothx andB.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, 01003, Amherst, MA, USA

    Jay Rosen

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  1. Jay Rosen
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Communicated by A. Jaffe

Partially supported by NSF-MCS-80-02940

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Rosen, J. A local time approach to the self-intersections of Brownian paths in space. Commun.Math. Phys. 88, 327–338 (1983). https://doi.org/10.1007/BF01213212

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  • DOI: https://doi.org/10.1007/BF01213212

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