International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1996 / Article

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Volume 9 |Article ID 919451 | 19 pages | https://doi.org/10.1155/S1048953396000445

Balls left empty by a critical branching Wiener process

Pál Révész1

1Technische Universität Wien, Institut für Statistik und Wahrscheinlichkeitstheorie, Austria

Received01 Jul 1996
Revised01 Oct 1996

Abstract

At time t=0 we have a Poisson random field on ℝd. Each particle executes a critical branching Wiener process starting from its position at time t=0. Let RT be the radius of the largest ball around the origin of ℝd which does not contain any particle at time T. Our goal is to characterize the properties of the stochastic process {RT,T≥0}.This article is dedicated to the memory of Professor Roland L. Dobrushin.

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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