数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 109-116.doi: 10.1016/S0252-9602(11)60213-0

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EQUIVALENT CONDITIONS OF LOCAL ASYMPTOTICS FOR THE OVERSHOOT OF A RANDOM WALK WITH HEAVY-TAILED INCREMENTS

王开永1,2|王岳宝1|尹传存3   

  1. 1. Department of Mathematics, Soochow University, Suzhou 215006, China; 2. School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China; 3. Department of Mathematics, Qufu Normal University, Qufu 273165, China
  • 收稿日期:2009-04-23 出版日期:2011-01-20 发布日期:2011-01-20
  • 基金资助:

    This work was supported by National Science Foundation of China (10671139, 11071182, 10771119), Natural Science Foundation of Jiangsu Highter Eduction Institution of China (10KJB110010),  and the research foundation of SUST.

EQUIVALENT CONDITIONS OF LOCAL ASYMPTOTICS FOR THE OVERSHOOT OF A RANDOM WALK WITH HEAVY-TAILED INCREMENTS

 WANG Kai-Yong1,2, WANG Yue-Bao1, YIN Chuan-Cun3   

  • Received:2009-04-23 Online:2011-01-20 Published:2011-01-20
  • Supported by:

    This work was supported by National Science Foundation of China (10671139, 11071182, 10771119), Natural Science Foundation of Jiangsu Highter Eduction Institution of China (10KJB110010),  and the research foundation of SUST.

摘要:

This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments,
from which we find that the above asymptotics are different from the local asymptotics for the supremum of the random walk. To do
this, the article first extends and improves some existing results about the solutions of renewal equations.

关键词: Equivalent conditions, asymptotics, random walk, renewal equation

Abstract:

This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments,
from which we find that the above asymptotics are different from the local asymptotics for the supremum of the random walk. To do
this, the article first extends and improves some existing results about the solutions of renewal equations.

Key words: Equivalent conditions, asymptotics, random walk, renewal equation

中图分类号: 

  • 60K05