Paper Info
Title
On Approximations and Ergodicity Classes in Random Chains.
Abstract
We study the limiting behavior of a random dynamic system driven by a stochastic chain. Our interest is in the chains that are not necessarily ergodic but are decomposable into ergodic classes. To investigate the conditions under which the ergodic classes of a model can be identified, we introduce and study an l 1 -approximation and infinite flow graph of the model. We show that the l 1 -approximations of random chains preserve certain limiting behavior. Using the l 1 -approximations, we show how the connectivity of the infinite flow graph is related to the structure of the ergodic groups of the model. Our main result of this paper provides conditions under which the ergodicity groups of the model can be identified by considering the connected components in the infinite flow graph. We provide two applications of our main result to random networks, namely broadcast over time-varying networks and networks with random link failure.
Year
DOI
Venue
2012
10.1109/TAC.2012.2191178
IEEE Trans. Automat. Contr.
Keywords
Field
DocType
Vectors,Stochastic processes,Modeling,Limiting,Indexes,Approximation methods,Stability analysis
Discrete mathematics,Ergodicity,Random graph,Control flow graph,Stationary ergodic process,Ergodic theory,Connected component,Conductance,Limiting,Mathematics
Journal
Volume
Issue
ISSN
57
11
0018-9286
Citations 
PageRank 
References 
13
0.86
17
Authors
2
Name
Order
Citations
PageRank
Behrouz Touri117621.12
Angelia Nedic22323148.65