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 ℓ1-approximation and infinite flow graph of the model. We show that the ℓ1-approximations of random chains preserve certain limiting behavior. Using the ℓ1-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.
- ergodicity classes
- infinite flow
- product of random matrices
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering