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Second order Subexponential Distributions with Finite Mean and Their Applications to Subordinated Distributions

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  • Jianxi Lin

    (Xiamen University)

Abstract

Consider a probability distribution subordinate to a subexponential distribution with finite mean. In this paper, we discuss the second order tail behavior of the subordinated distribution within a rather general framework in which we do not require the existence of density functions. For this aim, the so-called second order subexponential distribution is proposed and some of its related properties are established. Our results unify and improve some classical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:3:d:10.1007_s10959-010-0330-7
    DOI: 10.1007/s10959-010-0330-7
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    References listed on IDEAS

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    1. Søren Asmussen & Serguei Foss & Dmitry Korshunov, 2003. "Asymptotics for Sums of Random Variables with Local Subexponential Behaviour," Journal of Theoretical Probability, Springer, vol. 16(2), pages 489-518, April.
    2. Wang, Yuebao & Yang, Yang & Wang, Kaiyong & Cheng, Dongya, 2007. "Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 256-266, March.
    3. 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.
    4. 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.
    5. Omey, E. & Willekens, E., 1986. "Second order behaviour of the tail of a subordinated probability distribution," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 339-353, February.
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    Cited by:

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