设{X,X_n;n≥1}是一独立同分布的随机变量序列.如果|X_m|是新序列{|X_k|;k≤n}中的第r大元素,则令X_n^((r)=X_m.同时记部分和与修整和分别为S_n=sum from k=1 to n X_k和^((r))S_n=S_n-(X_n^((1))+…+X_n^((r))).该文在EX^2可能是无穷的条件下,得到了修整和^((r))S_n的广义强逼近定理.作为应用,建立了关于修整和以及修整和乘积的广义泛函重对数律.
For the large sparse saddle point problems, Pan and Li recently proposed in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31（3）： 231-242] a corrected Uzawa algorithm based on a nonlinear Uzawa algorithm with two nonlinear approximate inverses, and gave the detailed convergence analysis. In this paper, we focus on the convergence analysis of this corrected Uzawa algorithm, some inaccuracies in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31（3）： 231-242] are pointed out, and a corrected convergence theorem is presented. A special case of this modified Uzawa algorithm is also discussed.
Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.
