Limit theorems for some polynomial statistics of the Poisson process
type: Item
instance of: scholarly article
title: Limit theorems for some polynomial statistics of the Poisson process
zbMATH Open document ID: 0840.60025
DOI: 10.1007/BF00992616
author: Aleksandras Plikusas
published in: Acta Applicandae Mathematicae
publication date: 1996-06-30T00:00:00Z
review text: The central limit theorem and a theorem on large deviations are established for the distribution of a \(U\)-statistic of an inhomogeneous Poisson process \(X(t)\), \(0 \leq t \leq T\), as \(T \to \infty\). The proofs make use of formulas for the cumulants for this statistic and a general lemma of large deviations due to Saulis and Statulevičius.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 790352
zbMATH Keywords: stochastic integral
zbMATH Keywords: central limit theorem
zbMATH Keywords: large deviations
zbMATH Keywords: Poisson process
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 790352