Stochastic evolutionary system with Markov-modulated Poisson perturbations in the averaging schema
Artykuł w czasopiśmie
MNiSW
20
Lista 2024
| Status: | |
| Autorzy: | Semenyuk Serhiy A., Chabanyuk Yaroslav |
| Dyscypliny: | |
| Aby zobaczyć szczegóły należy się zalogować. | |
| Rok wydania: | 2024 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Numer czasopisma: | 1 |
| Wolumen/Tom: | 62 |
| Strony: | 102 - 108 |
| Scopus® Cytowania: | 0 |
| Bazy: | Scopus |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | TAK |
| Licencja: | |
| Sposób udostępnienia: | Otwarte czasopismo |
| Wersja tekstu: | Ostateczna wersja opublikowana |
| Czas opublikowania: | W momencie opublikowania |
| Data opublikowania w OA: | 15 września 2024 |
| Abstrakty: | angielski |
| This paper discusses the asymptotic behavior of the stochastic evolutionary system under the Markov-modulated Poisson perturbations in an averaging schema. Such a perturbation process combines the Poisson process with the Markov process that modulates the intensi- ty of jumps. This allows us to model systems with transitions between different modes or rare but significant jumps. Initially, the asymptotic properties of the Markov-modulated Poi- sson perturbation are investigated. For this purpose, we build the generator for the limit process solving the singular perturbation problem for the original process. Then we introduce a compensated Poisson process with a zero mean value, and it is used to center the jumps. The stochastic evolutionary system perturbed by the compensated Poisson process with an additional jump size function is described. We build the generator for an evolution process and investigate its asymptotic properties. Solving the singular perturbation problem we obtain the form of the limit process and its generator. This allows us to formulate and prove the theorem about weak convergence of the evolution process to the averaged one. The limit process for the stochastic evolutionary system at increasing time intervals is determined by the solution of a deterministic differential equation. The obtained result makes it possible to study the rate of convergence of the perturbed process to the limit one, as well as to consider stochastic approximation and optimization procedures for problems in which the system is described by an evolutionary equation with the Markov-modulated Poisson perturbation. |
