**Preface to "Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields"**

The evolution of the theory and applications of Markov chains has continued for over a century since 1907 when A. Markov stated the fundamental notion. Since then, it has evolved into one of the most important areas of stochastic processes and its applications have an immense diversity in various scientific fields. Miscellaneous generalizations and/or specializations have also given rise to emerging related fields and even support technologies such as artificial intelligence, or foster critical research in genetics. The present volume includes the papers published in the Journal of Mathematics in the Special Issue entitled "Markov and Semi-Markov chains, processes, systems and emerging related fields". The motivation was to assemble a collection of papers by well-known researchers in the field, aiming to provide advanced theoretical and applicable material for discussion, application and further research. In this respect, the volume covers a broad range of theory and applications on Markov and Semi-Markov systems, as well as the related stochastic processes. All papers underwent the peer-review process according to the standards of the Journal of Mathematics in the section of Probability and Statistics during the period from January to August 2021. A complete list of all articles, a short description, and useful introductory information about their particular research area can be found in the editorial of the book. Acknowledgments for this Special Issue and volume are due to many people, including the Chief Editors, the Editorial Board, the Authors, the Editorial Manager and Editorial stuff and are provided in detail in the editorial of the Special Issue.

> **Panagiotis-Christos Vassiliou, Andreas C. Georgiou** *Editors*
