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Second order tail behaviour of a subordinated probability distribution

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  • Geluk, J. L.

Abstract

Suppose G is a distribution function on [0, [infinity]) and F(x)=[summation operator][infinity]n=0pnG(n)(x)We prove necessary and sufficient conditions for the relations , where , and .

Suggested Citation

  • Geluk, J. L., 1992. "Second order tail behaviour of a subordinated probability distribution," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 325-337, March.
    • Handle: RePEc:eee:spapps:v:40:y:1992:i:2:p:325-337
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    Cited by:

    1. Geluk, J. L., 1996. "Tails of subordinated laws: The regularly varying case," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 147-161, January.
    2. Lin, Jianxi, 2012. "Second order asymptotics for ruin probabilities in a renewal risk model with heavy-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 422-429.
    3. Toshiro Watanabe, 2022. "Second-Order Behaviour for Self-Decomposable Distributions with Two-Sided Regularly Varying Densities," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1343-1366, June.
    4. Jianxi Lin, 2012. "Second order Subexponential Distributions with Finite Mean and Their Applications to Subordinated Distributions," Journal of Theoretical Probability, Springer, vol. 25(3), pages 834-853, September.
    5. Barbe, Ph. & McCormick, W.P. & Zhang, C., 2007. "Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1835-1847, December.
    6. Kortschak, Dominik & Albrecher, Hansjörg, 2010. "An asymptotic expansion for the tail of compound sums of Burr distributed random variables," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 612-620, April.

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