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arXiv · 1609.06701

Laws of Large Numbers for Supercritical Branching Gaussian Processes

Michael A. Kouritzin·Khoa Lê·Deniz Sezer
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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 with smaller Hurst parameter, are included as important examples. General branching with second moments is allowed and moment measure techniques are utilized.

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Michael A. Kouritzin, Khoa Lê, Deniz Sezer. 2016-09-21. Laws of Large Numbers for Supercritical Branching Gaussian Processes. https://arxiv.org/abs/1609.06701

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