Skip to main content
Article thumbnail
Location of Repository

Bounds on the deviation of discrete-time Markov chains from their mean-field model

By Luca Bortolussi A and Richard A. Hayden C

Abstract

We consider a generic mean-field scenario, in which a sequence of population models, described by discretetime Markov chains (DTMCs), converges to a deterministic limit in discrete time. Under the assumption that the limit has a globally attracting equilibrium, the steady states of the sequence of DTMC models converge to the point-mass distribution concentrated on this equilibrium. In this paper we provide explicit bounds in probability for the convergence of such steady states, combining stochastic bounds on the local error with control-theoretic tools used in the stability analysis of perturbed dynamical systems to bound the global accumulation of error. We also adapt this method to compute bounds on the transient dynamics. The approach is illustrated by a wireless sensor network example. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.7615
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://pubs.doc.ic.ac.uk/mf-dt... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.