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Asymptotics of the invariant measure in mean field models with jumps

Borkar, Vivek Shripad and Sundaresan, Rajesh (2011) Asymptotics of the invariant measure in mean field models with jumps. In: 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 28-30 Sept. 2011, Monticello, IL.

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Official URL: http://dx.doi.org/10.1109/Allerton.2011.6120312

Abstract

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Item Type: Conference Paper
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Additional Information: Copyright of this article belongs to IEEE.
Keywords: McKean-Vlasov Equation; Decoupling Approximation; Fluid Limit; Invariant Measure; Mean Field limit; Small Noise Limit; Stationary Measure; Stochastic Liouville Equation
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 28 Mar 2013 06:50
Last Modified: 28 Mar 2013 06:50
URI: http://eprints.iisc.ernet.in/id/eprint/46127

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