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A renormalized local time for multiple intersections of planar brownian motion

  • Jay Rosen
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1204)

Abstract

We present a simple prescription for ‘renormalizing’ the local time for n-fold intersections of planar Brownian motion, generalizing Varadhan's formula for n=2. In the latter case, we present a new proof that the renormalized local time is jointly continuous.

Keywords

Brownian Motion Local Time Dominate Convergence Theorem Springer Lecture Note Brownian Sheet 
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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Bibliography

  1. E. B. Dynkin [1985]-Random fields associated with multiple points of the Brownian motion, J. Funct. Anal. 62, 3.MathSciNetzbMATHGoogle Scholar
  2. J. F. Le Gall [1985]-Sur le temps local d'intersection du mouvement Brownien plan et la methode de renormalization de Varadhan, Séminare de Probabilities XIX. Springer Lecture Notes in Math, 1123.Google Scholar
  3. J. Rosen [1983]-A local time approach to the self-intersections of Brownian paths in space. Communications in Mathematical Physics, 88, 327–338.MathSciNetCrossRefzbMATHGoogle Scholar
  4. J. Rosen [1984a]-Self intersections of random fields, Annals of Probability 12, 108–119.MathSciNetCrossRefzbMATHGoogle Scholar
  5. J. Rosen [1984b]-Tanaka's formula and renormalization for intersections of planar Brownian motion, Annals of Probability. To appear.Google Scholar
  6. S. R. S. Varadhan [1969]-Appendix to Euclidean Quantum Field Theory by K. Symanzik, in Local Quantum Theory, R. Jost, Ed., Academic Press, N.Y.Google Scholar
  7. M. Yor [1985a]-Complements aux formules de Tanaka Rosen, Séminaire de Probabilities XIX, Springer Lecture Notes in Math, 1123.Google Scholar
  8. M. Yor "1985b]-Sur la répresentation comme intégrales stochastiques des temps d' occupation du mouvement brownien dans R d. In this volume.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

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

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