18 citations · 39 across the 15 of their papers we have counts for
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math.PR2011★ 6 cited
The exact asymptotic for the stationary distribution of some unreliable systems
Pawel Lorek
In this paper we find asymptotic distribution for some unreliable networks. Using Markov Additive Structure and Adan, Foley, McDonald method, we find the exact asymptotic for the s…
math.PR2011★ 1 cited
Strong Stationary Duality for Möbius Monotone Markov Chains: Unreliable Networks
Pawel Lorek, Ryszard Szekli
For Markov chains with a partially ordered finite state space we show strong stationary duality under the condition of Möbius monotonicity of the chain. We show relations of Möbius…
math.PR2011
Computable bounds on the spectral gap for unreliable Jackson networks
Pawel Lorek, Ryszard Szekli
The goal of this paper is to identify exponential convergence rates and to find computable bounds for them for Markov processes representing unreliable Jackson networks. First we u…