A note on Marked Point Processes and multivariate subordination

Petar Jevtic, Marina Marena, Patrizia Semeraro

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

The aim of this paper is to state a correspondence between marked Poisson processes and multivariate subordinated Lévy processes. We prove that, under suitable conditions, marked Poisson processes are in law subordinated Brownian motions and we provide their Lévy triplet and characteristic function. We introduce the class of multivariate Gaussian marked Poisson processes and prove that–in law–they are multivariate subordinated Brownian motions.

Original languageEnglish (US)
Pages (from-to)162-167
Number of pages6
JournalStatistics and Probability Letters
Volume122
DOIs
StatePublished - Mar 1 2017
Externally publishedYes

Keywords

  • Marked Poisson processes
  • Multivariate generalized asymmetric Laplace motion
  • Multivariate Poisson random measure
  • Multivariate subordinators
  • Subordinated Lévy processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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