Suppose {X,X n,n≥1} are the i.i.d. random variables with values in 2 type Banach space B,S n=∑nk=1X k,φ(x) is a increasing function on [0,+∞), φ(x)→+∞, and φ(x)x is no increasing; then we point out that the cl...Suppose {X,X n,n≥1} are the i.i.d. random variables with values in 2 type Banach space B,S n=∑nk=1X k,φ(x) is a increasing function on [0,+∞), φ(x)→+∞, and φ(x)x is no increasing; then we point out that the cluster set CS n2nφ(n) is ρK, where ρ= lim L 2nφ(n)<+∞, ∫ ∞e -ρ 2φ(x) 1xd x=+∞,X∈WM 2 0, and E‖X‖ 2φ(‖X‖)<+∞.展开更多
Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple coro...Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker.展开更多
Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probabil...Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.展开更多
文摘Suppose {X,X n,n≥1} are the i.i.d. random variables with values in 2 type Banach space B,S n=∑nk=1X k,φ(x) is a increasing function on [0,+∞), φ(x)→+∞, and φ(x)x is no increasing; then we point out that the cluster set CS n2nφ(n) is ρK, where ρ= lim L 2nφ(n)<+∞, ∫ ∞e -ρ 2φ(x) 1xd x=+∞,X∈WM 2 0, and E‖X‖ 2φ(‖X‖)<+∞.
文摘Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901138,11071213,11026087)supported by National Natural Science Foundation of China (Grant No.11071214)+1 种基金Natural Science Foundation of Zhejiang Province (Grant No.R6100119)Program for New Century Excellent Talents in University
文摘Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.
