CONVERGENCE-RATES FOR STOPPED RANDOM SUMS

[摘要] In this article we derive rates of convergence to normality for randomly stopped sums of suitably normalized i.d.d. random vectors in R(k). The summation indices tau(n) are assumed to be stopping times - an assumption which is often fulfilled in interesting applications such as sequential analysis, random walk problems and actuarial mathematics for which tau(n)/n converges in probability to a limit function r satisfying the moment condition integral(log(tau V e))(epsilon) dP < infinity for some epsilon > 0. Examples show that the convergence rates presented are sharp and that the moment condition imposed on the limit function tau cannot be dispensed with.

[发布日期] 1994-09-30

[关键词] SUMS OF INDEPENDENT RANDOM VARIABLES;SUMMATION INDEX DEPENDING ON SUMMANDS;RATES OF CONVERGENCE