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Using percolation on the branches of a Galton-Watson tree, Aldous and Pitman constructed by time-reversal in [4] an inhomogeneous tree-valued Markov process that starts from the
The boundary dimension of B [0 , 1] is the Hausdorff dimension of the “frontier” of Brownian motion, where the frontier of planar Brownian motion is t he boundary of the un-
Path transformations have proved useful in the study of Brownian motion and related pro- cesses, by providing simple constructions of various conditioned processes such as
By Skorokhod embedding of mean zero, finite variance random variables in Brownian motion, there is a stopping time τ such that for any standard Brownian motion (i.e., starting
Our main subjects in the present paper are divergence formulae for two types of Wiener spaces consisting of a Brownian motion starting from zero and a pinned Brownian motion
On the one hand, it is well-known from the work of Aldous [1] that the uniform random tree on a set of n vertices can be rescaled (specifically edges by a factor 1 / p n and masses
The expression just obtained for the distribution of coalescing Brownian motions is closely related to the formula for the transition density of the interlaced Brownian motions given
Lawler (1990): Non-intersection exponents for random walk and Brownian motion. Part II: Estimates and applications to a random
