On the Strong Laws of Large Numbers and the Rates of convergence for B-V alued Random Variable Sequences

摘要

Let {X_n,n>=1} be a sequence of independent B-valued random vandom variables, and G_p(x)=supn~-1Σ~n_I-1P(||X_I||~p>=x)(1<=p<2.). Under the condition ∫~∞_0 G_p(x)dx<∞, we Have n~-1/pΣ~n+I=1X_I→0 if and only if n~-1/pΣ~n+I=1Xi→0 a. s., and under similar conditions, the Rates of convergence and integability of partial sums of independent B-valued random Variable sequences are also discussed.