# Władysław SzczotkaUniversity of Wroclaw | WROC · Instytut Matematyczny

Władysław Szczotka

## About

8

Publications

138

Reads

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98

Citations

Citations since 2016

## Publications

Publications (8)

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 fu...

In this paper we derive Langevin picture of Lévy walks. Applying recent advances in the theory of coupled continuous time random walks we find a limiting process of the properly scaled Lévy walk. Next, we introduce extensions of Levy walks, in which jump sizes are some functions of waiting times. We prove that under proper scaling conditions, such...

An asymptotic behavior of a continuous-time random walk is investigated in the case when the sequence of pairs of jump vectors and times between jumps is chain dependent.

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...

This study establishes limiting distributions for customer waiting times and queue lengths in treelike networks with single-server nodes. The main result characterizes the limiting distributions when the network data (interarrival times, service times and routes) is "asymptotically stationary." This is a weak condition covering a variety of network...

The pair (W(t), L(t)t
( \frac1Öt W(t), \frac1Öt L(t) )\left( {\frac{1}{{\sqrt t }}W(t), \frac{1}{{\sqrt t }}L(t)} \right)
) conditioned on the event {T>t} is given ast, whereT is the length of the first busy period. A similar result is also given in the situation whent runs over the arrival moments of customers.

The paper deals with the asymptotic behaviour of queues for which the generic sequence is not necessarily stationary but is asymptotically stationary in some sense. The latter property is defined by an appropriate type of convergence of probability distributions of the sequences to the distribution of a stationary sequence We consider six types of...

## Projects

Project (1)

We consider max-AR(1) sequences of the Kendall type, because the distributions associated with them are heavy tailed and we apply them to air pollution modeling.
The main goals of the project:
-> Cramer-Lundberg model with applications of Kendall random walk;
-> Asymptotic properies of extremal Markovian sequences of the Kendall type;
-> Renewal theory for Kendall random walks ;
-> Wiener-Hopf factorization for max-AR(1) sequences of the Kendall type.