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}...

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Bibliographische Detailangaben
Veröffentlicht in:Advances in Applied Probability. - Applied Probability Trust. - 5(1973), 2, Seite 308-327
1. Verfasser: Stam, A. J. (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1973
Zugriff auf das übergeordnete Werk:Advances in Applied Probability
Schlagworte:Subordination Regular variation Convolution Tail behaviour Renewal theory Stable laws Attraction Mathematics Philosophy
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520 |a 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. 
540 |a Copyright 1973 Applied Probability Trust 
650 4 |a Subordination 
650 4 |a Regular variation 
650 4 |a Convolution 
650 4 |a Tail behaviour 
650 4 |a Renewal theory 
650 4 |a Stable laws 
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650 4 |a Mathematics  |x Pure mathematics  |x Geometry  |x Euclidean geometry  |x Geometric lines  |x Real lines 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Statistical theories  |x Law of large numbers 
650 4 |a Mathematics  |x Mathematical objects  |x Mathematical sequences 
650 4 |a Philosophy  |x Logic  |x Logical proofs 
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952 |d 5  |j 1973  |e 2  |h 308-327