Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications
This paper deals with discrete-time semi-Markov random evolutions (DTSMRE) in reduced random media. The reduction can be done for ergodic and non ergodic media. Asymptotic approximations of random evolutions living in reducible random media (random environment) are obtained. Namely, averaging, diffu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/6/963 |
| _version_ | 1797565524575518720 |
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| author | Nikolaos Limnios Anatoliy Swishchuk |
| author_facet | Nikolaos Limnios Anatoliy Swishchuk |
| author_sort | Nikolaos Limnios |
| collection | DOAJ |
| description | This paper deals with discrete-time semi-Markov random evolutions (DTSMRE) in reduced random media. The reduction can be done for ergodic and non ergodic media. Asymptotic approximations of random evolutions living in reducible random media (random environment) are obtained. Namely, averaging, diffusion approximation and normal deviation or diffusion approximation with equilibrium by martingale weak convergence method are obtained. Applications of the above results to the additive functionals and dynamical systems in discrete-time produce the above tree types of asymptotic results. |
| first_indexed | 2024-03-10T19:14:25Z |
| format | Article |
| id | doaj.art-caeab0373b3f4a4eab5c9de2f676df93 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T19:14:25Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-caeab0373b3f4a4eab5c9de2f676df932023-11-20T03:35:02ZengMDPI AGMathematics2227-73902020-06-018696310.3390/math8060963Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with ApplicationsNikolaos Limnios0Anatoliy Swishchuk1Sorbonne University Alliance, Université de Technologie de Compiègne, 60203 Compiègne, FranceDepartment of Mathematics and Statistics, Faculty of Science, University of Calgary, Calgary, AB T2N 1N4, CanadaThis paper deals with discrete-time semi-Markov random evolutions (DTSMRE) in reduced random media. The reduction can be done for ergodic and non ergodic media. Asymptotic approximations of random evolutions living in reducible random media (random environment) are obtained. Namely, averaging, diffusion approximation and normal deviation or diffusion approximation with equilibrium by martingale weak convergence method are obtained. Applications of the above results to the additive functionals and dynamical systems in discrete-time produce the above tree types of asymptotic results.https://www.mdpi.com/2227-7390/8/6/963semi-Markov chainrandom evolutionrandom mediareduced mediaaveragingdiffusion approximation |
| spellingShingle | Nikolaos Limnios Anatoliy Swishchuk Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications Mathematics semi-Markov chain random evolution random media reduced media averaging diffusion approximation |
| title | Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications |
| title_full | Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications |
| title_fullStr | Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications |
| title_full_unstemmed | Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications |
| title_short | Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications |
| title_sort | discrete time semi markov random evolutions in asymptotic reduced random media with applications |
| topic | semi-Markov chain random evolution random media reduced media averaging diffusion approximation |
| url | https://www.mdpi.com/2227-7390/8/6/963 |
| work_keys_str_mv | AT nikolaoslimnios discretetimesemimarkovrandomevolutionsinasymptoticreducedrandommediawithapplications AT anatoliyswishchuk discretetimesemimarkovrandomevolutionsinasymptoticreducedrandommediawithapplications |