A Markovian growth-collapse model
Autor(en): | Boxma, O Perry, D Stadje, W Zacks, S |
Stichwörter: | DAMS; DEPENDENCE; duality; growth-collapse process; hitting time; INPUT; Markov modulation; Mathematics; piecewise-deterministic Markov process; stationary distribution; Statistics & Probability; TIMES; uniform cut-off | Erscheinungsdatum: | 2006 | Herausgeber: | APPLIED PROBABILITY TRUST | Enthalten in: | ADVANCES IN APPLIED PROBABILITY | Band: | 38 | Ausgabe: | 1 | Startseite: | 221 | Seitenende: | 243 | Zusammenfassung: | We consider growth-collapse processes (GCPs) that grow linearly between random partial collapse times, at which they jump down according to some distribution depending on their current level. The jump occurrences are governed by a state-dependent rate function r(x). We deal with the stationary distribution of such a GCP, (X-t)(t >= 0), and the distributions of the hitting times T-a = inf{t >= 0: X-t = a}, a > 0. After presenting the general theory of these GCPs, several important special cases are studied. We also take a brief look at the Markov-modulated case. In particular, we present a method of computing the distribution of min[Ta, sigma] in this case (where sigma is the time of the first jump), and apply it to determine the long-run average cost of running a certain Markov-modulated disaster-ridden system. |
ISSN: | 00018678 | DOI: | 10.1239/aap/1143936148 |
Zur Langanzeige
Seitenaufrufe
4
Letzte Woche
1
1
Letzter Monat
2
2
geprüft am 07.06.2024