摘要:
给定取值于自然数集的随机过程
，类似于实数的连分数展式来定义随机连分数
，本文通过区间套定理证明了其收敛因子几乎必然地收敛到X，并对收敛因子的分母对应的Lévy常数进行了大偏差估计，在
满足独立同分布时，给出了相应概率的下界估计，对泊松分布、几何分布等特殊情形给出了具体的下界数值。
Abstract:
Given a stochastic process
, taking values in natural number. Analog to the continued fractions of real numbers, the random continued fraction
is defined. This paper shows that its convergent converges to X almost surely by the nest theorem for intervals. The large deviation estimate is also considered for the Lévy constant of the denominator of the convergents. When
is i.i.d., the lower bound for the corresponding probability is given. At the end, the exact lower bounds for Poission distribution, geometric process etc. are obtained.