重尾随机游动最大值的局部渐近性质及其在保险和排队论中的应用(英文)  

On local asymptotics for a heavy-tailed random walk maximum with applications in insurance and queueing theory

作　　者：明瑞星[1] 陈昱[1] 吴耀华[1] 

机构地区：[1]中国科学技术大学统计与金融系,安徽合肥230026

出　　处：《中国科学技术大学学报》2013年第3期173-181,共9页JUSTC

基　　金：Supported by National Science Foundation of China(10801124,11171321,10801188);the Fundamental Research Funds for the Central Universities(WK2040170006)

摘　　要：考虑一个随机游动Sn=X1+…+Xn,n=1,2,…,其中,X1,X2…独立同分布且有非负均值μ和共同分布F.对某个有限区间△,FS∈S△,给出了最大值M=max{S1,S2,…}属于区间(x,x+z]的概率的渐近性质,0<z<∞,x→∞.最后将该结论应用于保险和排队论中。A random walk Sn =X1 ＋X2 ＋… ＋Xn, n= 1,2,… was investigated where X1, X2, … are independent and identically distrbuted with negative mean m=EX and common distribution F. The asymptotic relationship was considered for the probability of the maximum M = max{S1, S2,…} which belongs to （x,x＋z] for some 0〈z〈∞ as x→∞ under the condition F^s∈ f△ for some finite interval △. Applications in insurance and queueing theory were also given.

关 键 词：随机游动 积分尾分布 局部次指数分布 破产概率 M G 1队列 GI G 1队列 

分 类 号：O212.1[理学—概率论与数理统计]