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


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Local Time 
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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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