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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…