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

Pál Révész

 Technische Universität Wien, Institut für Statistik und Wahrscheinlichkeitstheorie, Wien A-1040, Austria
Received 1 July 1996; Revised 1 October 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.