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Communications in Mathematical Physics

, Volume 88, Issue 3, pp 327–338 | Cite as

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

  • Jay Rosen
Article

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Local Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Jay Rosen
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA

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