W. Szczotka

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Let W = sup0≤t<∞(X(t)− βt), where X is a spectrally positive Lévy process with expectation zero and 0 < β < ∞. One of the main results of the paper says that for such a process X there exists a sequence of M/GI/1 queues for which stationary waiting times converge in distribution to W. The second result shows that condition (III) of Proposition 2 in the(More)
The paper gives some insight into the relations between two types of Markov processes – in the strict sense and in the wide sense – as well as into two aspects of periodicity. It concerns Markov processes with finite state space, the elements of which are complex numbers. Firstly it is shown that under some assumptions this space can be transformed in such(More)
We introduce a continuous-time random walk process with correlated temporal structure. The dependence between consecutive waiting times is generated by weighted sums of independent random variables combined with a reflecting boundary condition. The weights are determined by the memory kernel, which belongs to the broad class of regularly varying functions.(More)
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