On the universal constant in the Katz-Petrov and Osipov inequalities
Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.
On truncations for weakly ergodic inhomogeneous birth and death processes
Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin
Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, timedependent analysis is more meaningful....
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