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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
We prove that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean.. We show that
In [2] Aldous considers a tree constructed within the standard Brownian excursion, and shows that after conditioning on the occupation measure of the excursion, the law of the tree
We show that the sizes of the (rescaled) components converge to the excursion lengths of an inhomogeneous Brownian motion, which extends results of Aldous [1] for the critical
We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian
Remark 24 Recall that to prove Proposition 8, we used Proposition 1 to establish the fact that if there is a coalescent process satisfying conditions B1 and B2 of Theorem 2, then
Despite the fact that a solution to the stochastic game (3) has been explicitly characterised for the case that X is a linear Brownian motion in Kyprianou (2004), it turns out
In fact, for generalized integrated Brownian motions, the exact small ball asymptotics were obtained in [7] by different methods..
