Probability Theory and Related Fields

, Volume 92, Issue 4, pp 465–492 | Cite as

Local times on curves and uniform invariance principles

  • Richard F. Bass
  • Davar Khoshnevisan
Article
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Revised:

Summary

Sufficient conditions are given for a family of local times |L t µ | ofd-dimensional Brownian motion to be jointly continuous as a function oft and μ. Then invariance principles are given for the weak convergence of local times of lattice valued random walks to the local times of Brownian motion, uniformly over a large family of measures. Applications included some new results for intersection local times for Brownian motions on ℝ2 and ℝ2.

AMS Subject Classifications

60F17 60J55 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Richard F. Bass
    • 1
  • Davar Khoshnevisan
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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