TY - GEN
T1 - Products of stochastic matrices
T2 - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
AU - Bajovic, Dragana
AU - Xavier, Joao
AU - Sinopoli, Bruno
PY - 2012
Y1 - 2012
N2 - We find the large deviation rate I for convergence in probability of the product Wk C⋯W1W0 of temporally dependent random stochastic matrices. As the model for temporal dependencies, we adopt the Markov chain whose set of states is the set of all possible graphs that support the matrices Wk. Such model includes, for example, 1) token-based protocols, where a token is passed among nodes to determine the order of processing; and 2) temporally dependent link failures, where the temporal dependence is modeled by a Markov chain. We characterize the rate I as a function of the Markov chain transition probability matrix P. Examples further reveal how the temporal correlations (dependencies) affect the rate of convergence in probability I.
AB - We find the large deviation rate I for convergence in probability of the product Wk C⋯W1W0 of temporally dependent random stochastic matrices. As the model for temporal dependencies, we adopt the Markov chain whose set of states is the set of all possible graphs that support the matrices Wk. Such model includes, for example, 1) token-based protocols, where a token is passed among nodes to determine the order of processing; and 2) temporally dependent link failures, where the temporal dependence is modeled by a Markov chain. We characterize the rate I as a function of the Markov chain transition probability matrix P. Examples further reveal how the temporal correlations (dependencies) affect the rate of convergence in probability I.
UR - https://www.scopus.com/pages/publications/84875722938
U2 - 10.1109/Allerton.2012.6483290
DO - 10.1109/Allerton.2012.6483290
M3 - Conference contribution
AN - SCOPUS:84875722938
SN - 9781467345385
T3 - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
SP - 724
EP - 729
BT - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
Y2 - 1 October 2012 through 5 October 2012
ER -