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Fluctuations of extremal Markov chains of the Kendall type

Published in Arxiv preprint, 2019

Abstract: The paper deals with fluctuations of Kendall random walks, which are extremal Markov chains. We give the joint distribution of the first ascending ladder epoch and height over any level a >= 0 and distribution of maximum and minimum for these extremal Markovian sequences. We show that distribution of the first crossing time of level a > 0 is a mixture of geometric and negative binomial distributions. The Williamson transform is the main tool for considered problems connected with the Kendall convolution.

Recommended citation: B.H. Jasiulis-Gołdyn, M. Staniak, "Fluctuations of extremal Markov chains of the Kendall type", arxiv e-print, 2019. https://arxiv.org/abs/1902.00576

talks

Kendall Random Walks

Published:

Poster about Kendall random walk (with B. Jasiulis-Gołdyn, K. Łukaszewicz, W. Szczotka, M. Arendarczyk)

teaching

Programming and data analysis in R

Undergraduate course, University of Wrocław, Faculty of Mathematics and Computer Science, 2019

My introductory lab about programming and data wrangling + visualization in R (in polish).

Software development with R

Undergraduate course / graduate course, University of Wrocław, Faculty of Mathematics and Computer Science, 2020

My course on topics related to software engineering with R (in polish).