Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 531-549
doi:10.1155/S1048953396000445
Balls left empty by a critical branching Wiener process
Technische Universität Wien, Institut für Statistik und Wahrscheinlichkeitstheorie, Wien A-1040, Austria
Received 1 July 1996; Revised 1 October 1996
Copyright © 1996 Pál Révész. 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.
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.