On a Result of David Aldous Concerning the Trees in a Conditioned Excursion

Jon Warren (University of Warwick)

Abstract


The law of a random tree constructed within a Brownian excursion is calculated conditional on knowing the occupation measure of the excursion. In previous work David Aldous has used random walk approximations to obtain this result. Here it is deduced from Le Gall's description of the tree in the unconditioned excursion.

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Pages: 25-29

Publication Date: June 24, 1999

DOI: 10.1214/ECP.v4-1002

References

  1. D.J. Aldous, The continuum random tree III. Annals of Prob. 21(1):248-289, 1993. MR 94c:60015
  2. D.J. Aldous, Brownian excursion conditioned on its local time. Elect. Comm. in Probab. 3:79-90, 1998. Math Review number not available.
  3. J.F. Le Gall, The uniform random tree in the Brownian excursion. Prob. Th. Rel. Fields 96:369-383, 1993. MR 94e:60073
  4. D.Revuz and M.Yor, Continuous martingales and Brownian motion. Springer, 1998. MR 95h:60072
  5. J.Warren and M.Yor, The Brownian burglar: conditioning Brownian motion on its local time process. Seminaire de Prob. XXXII, 1998. Math Review number not available.
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