Another characterization of homogeneous Poisson processes. Issue 6 (18th August 2018)

• Record Type: Journal Article
• Authors: Vidmar, Matija
• Is Part Of: Stochastics. Volume 90:Issue 6(2018)
• Page Start: 876
• Page End: 885
• Publication Date: 2018-08-18
• Subjects: Renewal processes -- marking/thinning -- independence of first renewal epochs -- homogeneous Poisson processes; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2018.1457674
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract: For a general renewal process N (allowing delay, defect and multiple simultaneous arrivals) the independence of the first renewal epochs of the marked processes got from N by Bernoulli 0/1 thinning is characterized. This independence is well-known to hold true in the case of homogeneous Poisson processes; by way of corollary one obtains the interesting observation that, when coupled with some minimal extra conditions, it in fact already identifies them. The proof is analytic in character.