A note on Marked Point Processes and multivariate subordination

Petar Jevtić; Marina Marena; Patrizia Semeraro

doi:10.1016/j.spl.2016.11.008

A note on Marked Point Processes and multivariate subordination

Petar Jevtić, Marina Marena, Patrizia Semeraro

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	162-167
Number of pages	6
Journal	Statistics and Probability Letters
Volume	122
DOIs	https://doi.org/10.1016/j.spl.2016.11.008
State	Published - Mar 1 2017
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2016.11.008

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abstract = "The aim of this paper is to state a correspondence between marked Poisson processes and multivariate subordinated L{\'e}vy processes. We prove that, under suitable conditions, marked Poisson processes are in law subordinated Brownian motions and we provide their L{\'e}vy 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.",

keywords = "Marked Poisson processes, Multivariate Poisson random measure, Multivariate generalized asymmetric Laplace motion, Multivariate subordinators, Subordinated L{\'e}vy processes",

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AU - Jevtić, Petar

AU - Marena, Marina

AU - Semeraro, Patrizia

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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.

KW - Marked Poisson processes

KW - Multivariate Poisson random measure

KW - Multivariate generalized asymmetric Laplace motion

KW - Multivariate subordinators

KW - Subordinated Lévy processes

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SP - 162

EP - 167

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

A note on Marked Point Processes and multivariate subordination

Abstract

Keywords

ASJC Scopus subject areas

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