Markov Chains

László Lakatos, László Szeidl and Miklós Telek
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László Lakatos: Eötvös Loránd University
László Szeidl: Óbuda University
Miklós Telek: Budapest University of Technology and Economics

Chapter Chapter 3 in Introduction to Queueing Systems with Telecommunication Applications, 2013, pp 77-121 from Springer

Abstract: Abstract In the early twentieth century, Markov (1856–1922) introduced in [67] a new class of models called Markov chains, applying sequences of dependent random variables that enable one to capture dependencies over time. Since that time, Markov chains have developed significantly, which is reflected in the achievements of Kolmogorov, Feller, Doob, Dynkin, and many others. The significance of the extensive theory of Markov chains and the continuous-time variant called Markov processes is that it can be successfully applied to the modeling behavior of many problems in, for example, physics, biology, and economics, where the outcome of one experiment can affect the outcome of subsequent experiments. The terminology is not consistent in the literature, and many authors use the same name (Markov chain) for both discrete and continuous cases. We also apply this terminology.

Keywords: Homogeneous Markov Chain; Pointer Jumping; Null Recurrence; Homogeneous CTMCs; Discrete-time Markov Chain (DTMCs) (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-5317-8_3

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DOI: 10.1007/978-1-4614-5317-8_3

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