Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 531-549
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.
At time we have a Poisson random field on . Each particle executes
a critical branching Wiener process starting from its position at time . Let
be the radius of the largest ball around the origin of which does not
contain any particle at time . Our goal is to characterize the properties of the
stochastic process .
This article is dedicated to the memory of Professor Roland L. Dobrushin.