论文标题
LUROTH类型随机变量的加权总和的收敛性
Convergence for weighted sums of Luroth type random variables
论文作者
论文摘要
在这项工作中，我们证明了一个渐近结果，在涉及分布函数的某些条件下，对于任何Oppenheim扩展都是有效的，它扩展了W. Vervaat在1972年对LUROTH案例的分母证明的经典结果。此外，我们研究了独立随机变量序列的加权总和分布的收敛性。尽管结果是其自身感兴趣的，但在当前的环境中，它用于证明在LUROTH随机变量中获得的随机变量的特定序列的分布分布中的收敛性。
In this work we prove an asymptotic result, that under some conditions on the involved distribution functions, is valid for any Oppenheim expansion, extending a classical result proven by W. Vervaat in 1972 for denominators of the Luroth case. Furthermore, we study the convergence in distribution of weighted sums of a sequence of independent random variables. Although the result is of its own interest, in the present setting it is used to prove convergence in distribution of specific sequences of random variables generalizing known results obtained for Luroth random variables.
