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Functionals associated with self-intersections of the planar Brownian motion

  • E. B. Dynkin
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1204)

Abstract

For every k=1,2,3,...and for a wide class of measures λ, we construct a one-parameter family ℐk(λ, u), u≥0 of functionals of the planar Brownian motion (Xt,Pu) related to its self-intersections of multiplicity k during the time interval [0,u]. We investigate various families of functionals which converge to ℐk(λ,u) and we evaluate the moment functions Pμ[ℐk11,u) ...ℐknn,u)].

Keywords

Brownian Motion Random Field Joint Density Admissible Pair Initial Site 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • E. B. Dynkin
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaU.S.A.

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