Benutzer: Gast  Login
Dokumenttyp:
Zeitschriftenaufsatz 
Autor(en):
Kevei, P. 
Titel:
A note on the Kesten-Grincevičius-Goldie theorem 
Abstract:
Consider the perpetuity equation X=DAX+B, where (A,B) and X on the right-hand side are independent. The Kesten–Grincevičius–Goldie theorem states that if EAκ=1, EAκlog+A<∞, and E|B|κ<∞, then P{X>x}∼cx−κ. Assume that E|B|ν<∞ for some ν>κ, and consider two cases (i) EAκ=1, EAκlog+A=∞; (ii) EAκ<1, EAt=∞ for all t>κ. We show that under appropriate additional assumptions on A the asymptotic P{X>x}∼cx−κℓ(x) holds, where ℓ is a nonconstant slowly varying function. We use Goldie’s renewal theoretic approach. 
Stichworte:
perpetuity equation; stochastic difference equation; strong renewal theorem; expo- nential functional; maximum of random walk; implicit renewal theorem 
Zeitschriftentitel:
Electronic Communications in Probability 
Jahr:
2016 
Band / Volume:
21 
Jahr / Monat:
2016-07 
Quartal:
3. Quartal 
Monat:
Jul 
Heft / Issue:
51 
Seitenangaben Beitrag:
1-12 
Reviewed:
nein 
Sprache:
en 
Status:
Erstveröffentlichung 
TUM Einrichtung:
Lehrstuhl für Mathematische Statistik