Under α < d < (1+γ)α the centered and rescaled occupation-time process of a critical age-dependent branching system with Poisson immigration converges weakly in tempered distributions to a centered Gaussian process with explicit covariance that is self-similar and long-range dependent.
M.: Poisson random measures and super- critical multitype Markov branching processes.Stoch
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Occupation-Time Fluctuations of an Age-Dependent Branching System Driven by Poisson Immigration
Under α < d < (1+γ)α the centered and rescaled occupation-time process of a critical age-dependent branching system with Poisson immigration converges weakly in tempered distributions to a centered Gaussian process with explicit covariance that is self-similar and long-range dependent.