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150322s1973 xx |||||o 00| ||eng c |
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|a 10.2307/1426038
|2 doi
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|a (DE-627)JST000665592
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|a (JST)1426038
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|a DE-627
|b ger
|c DE-627
|e rakwb
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|a eng
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|a Stam, A. J.
|e verfasserin
|4 aut
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|a Regular Variation of the Tail of a Subordinated Probability Distribution
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|c 1973
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|a Text
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|a Computermedien
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|a Online-Ressource
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|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.
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|a Copyright 1973 Applied Probability Trust
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|a Subordination
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|a Regular variation
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|a Convolution
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|a Tail behaviour
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|a Renewal theory
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|a Stable laws
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|a Attraction
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Eigenfunctions
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|a Mathematics
|x Pure mathematics
|x Discrete mathematics
|x Number theory
|x Numbers
|x Real numbers
|x Rational numbers
|x Integers
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|a Mathematics
|x Pure mathematics
|x Geometry
|x Euclidean geometry
|x Geometric lines
|x Real lines
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|a Mathematics
|x Pure mathematics
|x Probability theory
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Statistical theories
|x Law of large numbers
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|a Mathematics
|x Mathematical objects
|x Mathematical sequences
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|a Philosophy
|x Logic
|x Logical proofs
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|a research-article
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|i Enthalten in
|t Advances in Applied Probability
|d Applied Probability Trust
|g 5(1973), 2, Seite 308-327
|w (DE-627)269247009
|w (DE-600)1474602-5
|x 00018678
|7 nnns
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|g volume:5
|g year:1973
|g number:2
|g pages:308-327
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|u https://www.jstor.org/stable/1426038
|3 Volltext
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|u https://doi.org/10.2307/1426038
|3 Volltext
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|d 5
|j 1973
|e 2
|h 308-327
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