mathematics Editorial Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields P.-C.G. Vassiliou 1, * and Andreas C. Georgiou 2, *   Citation: Vassiliou, P.-C.G.; Georgiou, A.C. Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields. Mathematics 2021, 9, 2490. https://doi.org/10.3390/ math9192490 Received: 25 September 2021 Accepted: 26 September 2021 Published: 4 October 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Statistical Science, University College London, Gower St, London WC1E 6BT, UK 2 Quantitative Methods and Decision Analysis Lab, Department of Business Administration, University of Macedonia, 54636 Thessaloniki, Greece * Correspondence: vasiliou@math.auth.gr (P.-C.G.V.); acg@uom.edu.gr (A.C.G.) Probability resembles the ancient Roman God Janus since, like Janus, probability also has a face with two different sides, which correspond to the metaphorical gateways and transitions between the past and the future. Probability can be seen as a limbo state between abstractness and concreteness. This inherent duality renders one side the closest possible to a branch of pure mathematics, derived from certain axioms in classical areas of algebra. Nonetheless, with its other side, probability is, indeed, an applied or applicable math- ematics discipline, most commonly known as applied probability, although, in our opinion, the common distinction between pure and applied mathematics is, all too often, merely artificial and, at times, fuzzy. This side, without being less demanding in mathematical or stochastic terms, gives birth to valuable models for studying everyday phenomena of the real world. Stochastic processes are, by now, well established as an extension of probability theory. In the area of stochastic processes, Markov and semi-Markov processes play a vital role as an independent area of study, generating important and novel applications and new mathematical results. The special issue with the title Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields includes fourteen articles published in the journal of “Mathe- matics” in the section of “Probability and Statistics”, in the period from January–August 2021. The authors of this issue acted as Academic Editors to all the papers except their own papers for which the Editorial Board appointed Academic Editors that were unknown to the authors and became known after the publication and after they agreed to their names being published. We hope that this volume provides opportunities for future research ideas and that the interested reader will discover these paths between the lines and the mathematical formulas of the published papers. The Guest Editors would like to thank the Chief Editors and the Editorial Board of the Journal of Mathematics for their invitation to edit the present volume. We cordially thank the authors for contributing to the publication of the volume by submitting their significant research articles and addressing all comments and suggestions with diligence and enthusiasm. We also pay our respects to the anonymous reviewers of the volume since, without their valuable assistance, this venture could have not been completed. We would also like to express our gratitude to the Editorial Manager, Dr. Syna Mu, for his continuous efforts to facilitate the workflow of this issue, for the excellent collaboration with the Guest Editors, and for arranging for the partial funding of the publication of the present volume. The Guest Editors would also like to thank the Professors Andras Telecs and Alexander Zeifman for acting as Academic Editors for our own contributed articles. Last, but not least, many thanks are due to the numerous Editorial Assistants who successfully undertook the tedious tasks of managing the large number of submissions in the present volume. We now proceed to a brief presentation of the articles by categorizing them in three sub-areas and also provide the reader with some useful references that might introduce Mathematics 2021, 9, 2490. https://doi.org/10.3390/math9192490 https://www.mdpi.com/journal/mathematics