论文标题
算法上随机序列及其收敛的绝对速度极限的大数字定律有效
An effectivization of the law of large numbers for algorithmically random sequences and its absolute speed limit of convergence
论文作者
论文摘要
大量定律是算法随机无限序列应该满足的基本特性之一。在本文中，我们表明，相对于任意可计算的Bernoulli度量，大量定律可以为任意的Schnorr随机无限序列而有效。此外，我们表明，在这种有效化中存在收敛的绝对速度限制，并且在某种意义上等于2。在本文中，我们还提供了大量强大定律中几乎确定的收敛的相应有效性，并且在概率理论的背景下，相对于大量的概率空间和i.i.d.它们上的随机变量不一定是可计算的。
The law of large numbers is one of the fundamental properties which algorithmically random infinite sequences ought to satisfy. In this paper, we show that the law of large numbers can be effectivized for an arbitrary Schnorr random infinite sequence, with respect to an arbitrary computable Bernoulli measure. Moreover, we show that an absolute speed limit of convergence exists in this effectivization, and it equals 2 in a certain sense. In the paper, we also provide the corresponding effectivization of almost sure convergence in the strong law of large numbers, and its absolute speed limit of convergence, in the context of probability theory, with respect to a large class of probability spaces and i.i.d. random variables on them, which are not necessarily computable.
