- Tytuł:
- On the Bochner subordination of exit laws
- Autorzy:
-
Hmissi, M.
Maaouia, W. - Powiązania:
- https://bibliotekanauki.pl/articles/254917.pdf
- Data publikacji:
- 2011
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
sub-Markovian semigroup
exit law
subordinator
Bernstein function
Bochner subordination - Opis:
- Let P = (Pt)t≥0 be a sub-Markovian semigroup on L2(m), let β = (βt)t≥0 be a Bochner subordinator and let Pβ = (Pβ(t ))t≥0 be the subordinated semigroup of P by means of β, i.e. Pβ(s):= ∫∞(0) Pr βs(dr). Let φ:= (φt)t>0 be a P-exit law, i.e. Ptφs = φs+t, s,t>0 and let φβ(t):= ∫∞(0)φs βt(ds). Then φβ:= (φβ(t)t>0 is a Pβ-exit law whenever it lies in L2(m). This paper is devoted to the converse problem when β is without drift. We prove that a Pβ-exit law ψ:= (ψt)t>0 is subordinated to a (unique) P-exit law φ (i.e. ψ= φ β) if and only if (Ptu)t>0 ⊂ D(Aβ), where u = ∫∞(0)e-s ψ sds and Aβ, is the L2(m)-generator of Pβ.
- Źródło:
-
Opuscula Mathematica; 2011, 31, 2; 195-207
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł