指标在T_θ~d上变动的B-值I.I.D.R.V.’S的叠对数律

THE LAW OF THE ITERATED LOGARITHM FOR B-VALUED I. I. D. R. V.' S INDEXED BY T_(?)~d

记B是可分Banach空间,X是B-值随机变量,N^d={■=n_1,…,n_d);n_i=1,2,…,i=1,…,d},T_θ~d={■∈=(n_1,…,n_d),θn_i≤n_y≤θ^(-1)n_4,i≠j,i,j=1,…,d},其中d≥2,0<1。本文研究指标在T_θ~d上变动的B-值i. i. d. r. v. ’s的四种类型的叠对数律(即BLIL^(θ,α)_1,BLIL^(θ,d)_2CLIL^(θ.D)_1和GLIL^(θ,d)_2,获得了X∈BLIL^(θ,α)_1、X∈BLIL^(θ,d)_2、X∈GLIL^(θ,d)_1和X∈GLIL^(θ,d)_2的充要条件。

Let B be a real separable Banach space and X a B-valued random variable. Set N^d={=(n_1,…,n_d);n_i=1, 2, …,i=1, …, d} and T_θ~d={=(n_1,…,n_d)∈N^d; θn_i≤n_j≤ θ^(-1)n_i, i≠j, i, j=1,…, d}, where d≥2 and 0<θ<1. In this paper, we discuss four forms of the LIL for B-valued i.i.d.r.v.' s indexed by T_θ~i (i.e. BLIL^((θ,d)_2), BLIL^((θ,d)_2), CLI L^((θ,d)_2) and CLIL^((θ,d)_2)) and obtain necessary and sufficient conditions for X to satisfy, respectively, BLIL^((θ,d)_2), BLIL^((θ,d)_2), CLIL^((θ,d)_2) and CLIL^((θ,d)_2).