【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。更多还原

【Abstract】 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 Fs∈S△ for some finite interval △.Applications in insurance and queueing theory were also given.更多还原