Laws of large numbers for supercritical branching Gaussian processes

A general class of non-Markov, supercritical Gaussian branching particle systems is introduced and its long-time asymptotics is studied. Both weak and strong laws of large numbers are developed with the limit object being characterized in terms of particle motion/mutation. Long memory processes, lik...

Full description

Saved in:
Bibliographic Details
Published inStochastic processes and their applications Vol. 129; no. 9; pp. 3463 - 3498
Main Authors Kouritzin, Michael A., Lê, Khoa, Sezer, Deniz
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2019
Subjects
Branching processes
Fractional Brownian motion
Laws of large numbers
secondary
Laws of large numbers
Branching processes
Fractional Brownian motion
primary
Online AccessGet full text

Cover

More Information
Summary:A general class of non-Markov, supercritical Gaussian branching particle systems is introduced and its long-time asymptotics is studied. Both weak and strong laws of large numbers are developed with the limit object being characterized in terms of particle motion/mutation. Long memory processes, like branching fractional Brownian motion and fractional Ornstein–Uhlenbeck processes with large Hurst parameters, as well as rough processes, like fractional processes with smaller Hurst parameter, are included as important examples. General branching with second moments is allowed and moment measure techniques are utilized.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2018.09.011