Renewal theory for extremal Markov sequences of Kendall type

Barbara Jasiulis-gołdyn , Jolanta Misiewicz , Karolina Naskręt , Edward Omey

Abstract

The paper deals with renewal theory for a class of extremal Markov sequences connected with the Kendall convolution. We consider here some particular cases of the Wold processes associated with generalized convolutions. We prove an analogue of the Fredholm theorem for all regular generalized convolutions algebras. Using regularly varying functions we prove a Blackwell theorem and a limit theorem for renewal processes defined by Kendall random walks. Our results set new research hypotheses for other generalized convolution algebras to investigate renewal processes constructed by Markov processes with respect to generalized convolutions.
Author Barbara Jasiulis-gołdyn (FMIS)
Barbara Jasiulis-gołdyn,,
- Faculty of Mathematics and Information Science
, Jolanta Misiewicz (FMIS)
Jolanta Misiewicz,,
- Faculty of Mathematics and Information Science
, Karolina Naskręt
Karolina Naskręt,,
-
, Edward Omey
Edward Omey,,
-
Journal seriesStochastic Processes and their Applications, ISSN 0304-4149, e-ISSN 1879-209X
Issue year2020
Vol130
No6
Pages3277-3294
Publication size in sheets0.85
Keywords in EnglishKendall random walk, Renewal theory, Regularly varying function, Fredholm theorem, Blackwell theorem, Wold process
ASJC Classification2604 Applied Mathematics; 2611 Modelling and Simulation; 2613 Statistics and Probability
DOIDOI:10.1016/j.spa.2019.09.013
URL https://www.sciencedirect.com/science/article/pii/S0304414918304010
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 30-06-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.177; WoS Impact Factor: 2018 = 1.342 (2) - 2018=1.455 (5)
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