Acta mathematica scientia, Series B >
EQUIVALENT CONDITIONS OF LOCAL ASYMPTOTICS FOR THE OVERSHOOT OF A RANDOM WALK WITH HEAVY-TAILED INCREMENTS
Received date: 2009-04-23
Online 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.
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
WANG Kai-Yong , WANG Yue-Bao , YIN Chuan-Cun . EQUIVALENT CONDITIONS OF LOCAL ASYMPTOTICS FOR THE OVERSHOOT OF A RANDOM WALK WITH HEAVY-TAILED INCREMENTS[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 109 -116 . DOI: 10.1016/S0252-9602(11)60213-0
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