Asymptotics of random processes with immigration. II: Convergence to stationarity.

DOI10.3150/15-BEJ777zbMath1377.60046arXiv1311.6923OpenAlexW2964329032MaRDI QIDQ520699

Alexander Marynych, Matthias Meiners, Aleksander M. Iksanov

Publication date: 5 April 2017

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.6923

zbMATH Keywords

renewal shot noise processrandom point processstationary renewal processweak convergence in the Skorokhod space

Mathematics Subject Classification ID

Sample path properties (60G17) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Renewal theory (60K05)

Related Items (9)

A functional limit theorem for random processes with immigration in the case of heavy tails ⋮ Functional limit theorems for a new class of non-stationary shot noise processes ⋮ A functional limit theorem for general shot noise processes ⋮ Functional Limit Theorems for Shot Noise Processes with Weakly Dependent Noises ⋮ Moments of the stationary distribution of subcritical multitype Galton-Watson processes with immigration ⋮ Stationary limits of shot noise processes ⋮ Shot noise, weak convergence and diffusion approximations ⋮ Shot noise processes with randomly delayed cluster arrivals and dependent noises in the large-intensity regime ⋮ On the local time of a recurrent random walk on ℤ²

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