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.
