Asymptotics of the invariant measure in mean field models with jumps


Autoria(s): Borkar, Vivek Shripad; Sundaresan, Rajesh
Data(s)

2011

Resumo

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.

Formato

application/pdf

Identificador

http://eprints.iisc.ernet.in/46127/1/Com_Con_Com_1258_2011.pdf

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.

Publicador

IEEE

Relação

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

http://eprints.iisc.ernet.in/46127/

Palavras-Chave #Electrical Communication Engineering
Tipo

Conference Paper

PeerReviewed