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Equivalent Conditions of Asymptotics for the Density of the Supremum of a Random Walk in the Intermediate Case

Author

Listed:
  • Yuebao Wang

    (Soochow University)

  • Kaiyong Wang

    (Soochow University
    Suzhou University of Science and Technology)

Abstract

This paper obtains some equivalent conditions about the asymptotics for the density of the supremum of a random walk with light-tailed increments in the intermediate case. To do this, the paper first corrects the proofs of some existing results about densities of random sums. On the basis of the above results, the paper obtains some equivalent conditions about the asymptotics for densities of ruin distributions in the intermediate case and densities of infinitely divisible distributions. In the above studies, some differences and relations between the results on a distribution and its corresponding density can be discovered.

Suggested Citation

  • Yuebao Wang & Kaiyong Wang, 2009. "Equivalent Conditions of Asymptotics for the Density of the Supremum of a Random Walk in the Intermediate Case," Journal of Theoretical Probability, Springer, vol. 22(2), pages 281-293, June.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:2:d:10.1007_s10959-009-0217-7
    DOI: 10.1007/s10959-009-0217-7
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    References listed on IDEAS

    as
    1. Korshunov, D., 1997. "On distribution tail of the maximum of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 97-103, December.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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