Balls left empty by a critical branching Wiener process. (1996)

• Record Type: Journal Article
• Authors: Révész, Pál
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 9:Number 4(1996)
• Page Start: 531
• Page End: 549
• Publication Date: 1996
• Subjects: branching random process -- branching random fields -- strong laws; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953396000445
• Languages: English
• ISSNs: 1048-9533

Abstract

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