Random Brownian Scaling Identities
نویسندگان
چکیده
An identity in distribution due to F. Knight for Brownian motion is extended in two diierent ways: rstly by replacing the supremum of a reeecting Brownian motion by the range of an unreeected Brownian motion, and secondly by replacing the reeecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excursions. The rst extension is related to two diierent constructions of It^ o's law of Brownian excursions, due to D. Williams and J.-M. Bismut, each involving back-to-back splicing of fragments of two independent three-dimensional Bessel processes. Generalizations of both splicing constructions are described which involve Bessel processes and Bessel bridges of arbitrary positive real dimension.
منابع مشابه
Random Brownian Scaling Identities and Splicing of Bessel Processes
An identity in distribution due to F. Knight for Brownian motion is extended in two di erent ways: rstly by replacing the supremum of a re ecting Brownian motion by the range of an unre ected Brownian motion, and secondly by replacing the re ecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excurs...
متن کاملBrownian Motion, Bridge, Excursion, and Meander Characterized by Sampling at Independent Uniform Times
For a random process X consider the random vector deened by the values of X at times 0 < U n;1 < ::: < U n;n < 1 and the minimal values of X on each of the intervals between consecutive pairs of these times, where the U n;i are the order statistics of n independent uniform (0; 1) variables, independent of X. The joint law of this random vector is explicitly described when X is a Brownian motion...
متن کاملMeander Characterized by Sampling at Independent Uniform Times
For a random process X consider the random vector defined by the values of X at times 0 < Un,1 < ... < Un,n < 1 and the minimal values of X on each of the intervals between consecutive pairs of these times, where the Un,i are the order statistics of n independent uniform (0, 1) variables, independent of X. The joint law of this random vector is explicitly described when X is a Brownian motion. ...
متن کاملDynamics for the Brownian Web and the Erosion Flow
Abstract. The Brownian web is a random object that occurs as the scaling limit of an infinite system of coalescing random walks. Perturbing this system of random walks by, independently at each point in space-time, resampling the random walk increments, leads to some natural dynamics. In this paper we consider the corresponding dynamics for the Brownian web. In particular, pairs of coupled Brow...
متن کاملTHE BROWNIAN NET By Rongfeng Sun and Jan
The (standard) Brownian web is a collection of coalescing onedimensional Brownian motions, starting from each point in space and time. It arises as the diffusive scaling limit of a collection of coalescing random walks. We show that it is possible to obtain a nontrivial limiting object if the random walks in addition branch with a small probability. We call the limiting object the Brownian net,...
متن کامل