A Continuous-Time Semi-Markov System Governed by Stepwise Transitions
In this paper, we introduce a class of stochastic processes in continuous time, called step semi-Markov processes. The main idea comes from bringing an additional insight to a classical semi-Markov process: the transition between two states is accomplished through two or several steps. This is an ex...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2745 |
| _version_ | 1797413039918546944 |
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| author | Vlad Stefan Barbu Guglielmo D’Amico Andreas Makrides |
| author_facet | Vlad Stefan Barbu Guglielmo D’Amico Andreas Makrides |
| author_sort | Vlad Stefan Barbu |
| collection | DOAJ |
| description | In this paper, we introduce a class of stochastic processes in continuous time, called step semi-Markov processes. The main idea comes from bringing an additional insight to a classical semi-Markov process: the transition between two states is accomplished through two or several steps. This is an extension of a previous work on discrete-time step semi-Markov processes. After defining the models and the main characteristics of interest, we derive the recursive evolution equations for two-step semi-Markov processes. |
| first_indexed | 2024-03-09T05:11:48Z |
| format | Article |
| id | doaj.art-36d3a07e094a443e9063b8b13397ba12 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:11:48Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-36d3a07e094a443e9063b8b13397ba122023-12-03T12:48:19ZengMDPI AGMathematics2227-73902022-08-011015274510.3390/math10152745A Continuous-Time Semi-Markov System Governed by Stepwise TransitionsVlad Stefan Barbu0Guglielmo D’Amico1Andreas Makrides2Laboratory of Mathematics Raphaël Salem, University of Rouen-Normandy, UMR 6085, Avenue de l’Université, BP.12, F-76801 Saint-Étienne-du-Rouvray, FranceDepartment of Economics, University “G. d’Annunzio” of Chieti-Pescara, Viale Pindaro 42, 65127 Pescara, ItalyDepartment of Statistics and Actuarial-Financial Mathematics, University of the Aegean, GR-83200 Samos, GreeceIn this paper, we introduce a class of stochastic processes in continuous time, called step semi-Markov processes. The main idea comes from bringing an additional insight to a classical semi-Markov process: the transition between two states is accomplished through two or several steps. This is an extension of a previous work on discrete-time step semi-Markov processes. After defining the models and the main characteristics of interest, we derive the recursive evolution equations for two-step semi-Markov processes.https://www.mdpi.com/2227-7390/10/15/2745continuous-time semi-Markov processesstep semi-Markov processesminimum class of distributionsstochastic modelling |
| spellingShingle | Vlad Stefan Barbu Guglielmo D’Amico Andreas Makrides A Continuous-Time Semi-Markov System Governed by Stepwise Transitions Mathematics continuous-time semi-Markov processes step semi-Markov processes minimum class of distributions stochastic modelling |
| title | A Continuous-Time Semi-Markov System Governed by Stepwise Transitions |
| title_full | A Continuous-Time Semi-Markov System Governed by Stepwise Transitions |
| title_fullStr | A Continuous-Time Semi-Markov System Governed by Stepwise Transitions |
| title_full_unstemmed | A Continuous-Time Semi-Markov System Governed by Stepwise Transitions |
| title_short | A Continuous-Time Semi-Markov System Governed by Stepwise Transitions |
| title_sort | continuous time semi markov system governed by stepwise transitions |
| topic | continuous-time semi-Markov processes step semi-Markov processes minimum class of distributions stochastic modelling |
| url | https://www.mdpi.com/2227-7390/10/15/2745 |
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