一类非标准随机游动及其在风险理论中的应用

A Class of Non-Standard Random Walks with Applications to Risk Theory

考虑一类非标准的随机游动Sn=X1+…+Xn,其中Xi(i≥1)为一列独立的随机变量序列,X1的分布函数为G,Xi(i≥2)具有共同的分布函数F.本文主要研究了F与G属于S(γ)族时,非标准随机游动的尾等价式和局部等价式,并给出在风险理论中的一些应用.

This paper studies a class of non-standard random walk, Sn = X1 ＋ ... ＋ Xn, where Xi （i≥1） is a sequence of independent random variables, and X1 has a distributin G, Xi （i≥2） have the common distribution F. Under the assumption that the distributions of the summands belong to S（γ）, we obtain a local asymptotic estimate and a tail asymptotic estimate for the distribution of maximum of Sn. Applications in risk theory are investigated.