Laws of large numbers for supercritical branching Gaussian processes

Michael A. Kouritzin, Khoa Lê and Deniz Sezer

Stochastic Processes and their Applications, 2019, vol. 129, issue 9, 3463-3498

Abstract: 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.

Keywords: Fractional Brownian motion; Branching processes; Laws of large numbers (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.09.011

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