IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i5-6p462-472.html
   My bibliography  Save this article

The closure of the convolution equivalent distribution class under convolution roots with applications to random sums

Author

Listed:
  • Yu, Changjun
  • Wang, Yuebao
  • Yang, Yang

Abstract

Let F be a proper distribution on D=[0,[infinity]) or (-[infinity],[infinity]) and N be a non-negative integer-valued random variable with masses . Denote . The main result of this paper is that under some suitable conditions, G belongs to the convolution equivalent distribution class if and only if F belongs to the convolution equivalent distribution class. As applications, some known results on random sums have been extended and improved, which give a positive answer under certain conditions to Problem 1 of Watanabe (2008). Similarly, some corresponding results for the local distributions and densities have been obtained.

Suggested Citation

  • Yu, Changjun & Wang, Yuebao & Yang, Yang, 2010. "The closure of the convolution equivalent distribution class under convolution roots with applications to random sums," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 462-472, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:462-472
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00448-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
    2. Gao, Qingwu & Wang, Yuebao, 2009. "Ruin probability and local ruin probability in the random multi-delayed renewal risk model," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 588-596, March.
    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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yu, Changjun & Wang, Yuebao & Cui, Zhaolei, 2010. "Lower limits and upper limits for tails of random sums supported on," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1111-1120, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhaolei Cui & Yuebao Wang & Hui Xu, 2022. "Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform," Mathematics, MDPI, vol. 10(21), pages 1-24, November.
    2. Yu, Changjun & Wang, Yuebao & Cui, Zhaolei, 2010. "Lower limits and upper limits for tails of random sums supported on," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1111-1120, July.
    3. Wang, Kaiyong & Yang, Yang & Yu, Changjun, 2013. "Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1504-1512.
    4. Geluk, J.L. & De Vries, C.G., 2006. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 39-56, February.
    5. 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.
    6. 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.
    7. Sgibnev, M. S., 2001. "Exact asymptotic behaviour of the distribution of the supremum," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 301-311, April.
    8. Braverman, Michael & Samorodnitsky, Gennady, 1995. "Functionals of infinitely divisible stochastic processes with exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 207-231, April.
    9. Toshiro Watanabe & Kouji Yamamuro, 2010. "Local Subexponentiality and Self-decomposability," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1039-1067, December.
    10. Danilenko, Svetlana & Šiaulys, Jonas, 2016. "Randomly stopped sums of not identically distributed heavy tailed random variables," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 84-93.
    11. 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.
    12. Toshiro Watanabe, 2021. "Two Hypotheses on the Exponential Class in the Class Of O-subexponential Infinitely Divisible Distributions," Journal of Theoretical Probability, Springer, vol. 34(2), pages 852-873, June.
    13. Horst, Ulrich, 2007. "Stochastic cascades, credit contagion, and large portfolio losses," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 25-54, May.
    14. Gao, Qingwu & Wang, Yuebao, 2009. "Ruin probability and local ruin probability in the random multi-delayed renewal risk model," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 588-596, March.
    15. Toshiro Watanabe & Kouji Yamamuro, 2017. "Two Non-closure Properties on the Class of Subexponential Densities," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1059-1075, September.
    16. Omey, Edward & Vesilo, R., 2009. "Random Sums of Random Variables and Vectors," Working Papers 2009/09, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    17. Schlegel, Sabine, 1998. "Ruin probabilities in perturbed risk models," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 93-104, May.
    18. Willmot, Gordon E., 1997. "On the relationship between bounds on the tails of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 19(2), pages 95-103, April.
    19. Griffin, Philip S., 2022. "Path decomposition of a reflected Lévy process on first passage over high levels," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 29-47.
    20. Vaios Dermitzakis & Susan M. Pitts & Konstadinos Politis, 2010. "Lundberg-type Bounds and Asymptotics for the Moments of the Time to Ruin," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 155-175, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:462-472. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.