Abstract
We consider a network in which a call holds a given number of uniformly chosen links and releases them simultaneously. We show pathwise propagation of chaos and convergence of the process of empirical fluctuations to a Gaussian Ornstein-Uhlenbeck process. The limiting martingale problem is obtained by closing a hierarchy. The drift term is given by a simple factorization technique related to mean-field interaction, but the Doob-Meyer bracket contains special terms coming from the strong interaction due to simultaneous release. This is treated by closing another hierarchy pertaining to a measure-valued process related to calls routed through couples of links, and the factorization is again related to mean-field interaction. Fine estimates obtained by pathwise interaction graph constructions are used for tightness purposes and are thus shown to be of optimal order.
Citation
Carl Graham. Sylvie Meleard. "Dynamic Asymptotic Results for a Generalized Star-Shaped Loss Network." Ann. Appl. Probab. 5 (3) 666 - 680, August, 1995. https://doi.org/10.1214/aoap/1177004700
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