18 citations · 39 across the 15 of their papers we have counts for
5 papers · 1 filter
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…
Some results on random design regression with long memory errors and predictors
Rafal Kulik, Pawel Lorek
This paper studies nonparametric regression with long memory (LRD) errors and predictors. First, we formulate general conditions which guarantee the standard rate of convergence fo…
Empirical process of residuals for regression models with long memory errors
Pawel Lorek, Rafal Kulik
We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are diffe…
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…
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…