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August, 1995 Dynamic Asymptotic Results for a Generalized Star-Shaped Loss Network
Carl Graham, Sylvie Meleard
Ann. Appl. Probab. 5(3): 666-680 (August, 1995). DOI: 10.1214/aoap/1177004700


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.


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Carl Graham. Sylvie Meleard. "Dynamic Asymptotic Results for a Generalized Star-Shaped Loss Network." Ann. Appl. Probab. 5 (3) 666 - 680, August, 1995.


Published: August, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0842.60091
MathSciNet: MR1359824
Digital Object Identifier: 10.1214/aoap/1177004700

Primary: 60K35
Secondary: 60F05 , 60F17 , 68M10 , 90B12

Keywords: Fluctuations , hierarchies , interaction graphs , networks , propagation of chaos

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 3 • August, 1995
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