随机变量序列的大数定律及常返性定理

Law of Large Numbers and Recurrence Theorem for Random Variable Sequence

对一类有界独立或相依的随机变量序列|ξn|,获得了它的伯努利大数定律、波雷尔强大数定律及常返性定理.作为应用,得出了Loève专著[1]中的推广的伯努利大数定律、常返性定理,改进了[1]中的推广的波雷尔强大数定律.

We obtain Bernoulli law of large numbers,Borel strong law of large numbers and recurrence theorem for bounded,independent or dependent random variable sequence {ξn}.As appllications,we get the extended Bernoulli law of large numbers,recurrence theorem in [1] and improves the extended Borel strong law of large numbers in [1].