Regular Variation of the Tail of a Subordinated Probability Distribution
Let F be a probability measure on the real line and G=Σ C(k)Fk*the probability measure subordinate to F with subordinator C restricted to the nonnegative integers. Let V(x) vary regularly of order ρ for x→ ∞ and either (1) V(x)F[x,∞)→ a≥ 0 or (2) $V(x)C[x,\infty)\rightarrow \gamma \geq 0.\ \text{If}...
| Veröffentlicht in: | Advances in Applied Probability. - Applied Probability Trust. - 5(1973), 2, Seite 308-327 |
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| 1. Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1973
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| Zugriff auf das übergeordnete Werk: | Advances in Applied Probability |
| Schlagworte: | Subordination Regular variation Convolution Tail behaviour Renewal theory Stable laws Attraction Mathematics Philosophy |
| Zusammenfassung: | Let F be a probability measure on the real line and G=Σ C(k)Fk*the probability measure subordinate to F with subordinator C restricted to the nonnegative integers. Let V(x) vary regularly of order ρ for x→ ∞ and either (1) V(x)F[x,∞)→ a≥ 0 or (2) $V(x)C[x,\infty)\rightarrow \gamma \geq 0.\ \text{If}\ \rho >1$ and F(-∞ ,0)=0, necessary and sufficient in order that V(x)G[x,∞)→ b, is that both (1) and (2) hold for suitable α and γ . For 0≤ ρ ≤ 1 the conditions are of different type. For two-sided F a different situation arises and only sufficient conditions are found. An application to renewal moments of negative order is given. |
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| ISSN: | 00018678 |
| DOI: | 10.2307/1426038 |