- Tytuł:
- The first exit of almost strongly recurrent semi-Markov processes
- Autorzy:
-
Domsta, Joachim
Grabski, Franciszek - Powiązania:
- https://bibliotekanauki.pl/articles/1340260.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
limit distribution
Markov renewal
first exit
extended exponential p.d
semi-Markov
recurrent Markov processes - Opis:
- Let $\stackrelnX(·)$, n ∈ N, be a sequence of homogeneous semi-Markov processes (HSMP) on a countable set K, all with the same initial p.d. concentrated on a non-empty proper subset J. The subrenewal kernels which are restrictions of the corresponding renewal kernels $\stackrelnQ$ on K×K to J×J are assumed to be suitably convergent to a renewal kernel P (on J×J). The HSMP on J corresponding to P is assumed to be strongly recurrent. Let [$π_j$; j ∈ J] be the stationary p.d. of the embedded Markov chain. In terms of the averaged p.d.f. $F_{ϑ}(t) :=\sum_{j,k ∈ J} π_jP_{j,k}(t)$, t ∈ i$ℝ_+$, and its Laplace-Stieltjes transform $\widetilde F_ϑ$, the above assumptions imply: The time $\stackrel{n}{T}_{J}$ of the first exit of $\stackrel{n}{X}(·)$ from J has a limit p.d. (up to some constant factors) iff 1 - $\widetilde F_ϑ$ is regularly varying at 0 with a positive degree, say α ∈ (0,1]. Then the transform of the limit p.d.f. equals $\widetilde G^{(α)}(s) = (1+s^{α})^{-1}$, Re s ≥ 0. This extends the results by V. S. Korolyuk and A. F. Turbin (1976) obtained for α = 1 under essentially stronger conditions.
- Źródło:
-
Applicationes Mathematicae; 1995-1996, 23, 3; 285-304
1233-7234 - Pojawia się w:
- Applicationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł