Convergence for weighted sums of Luroth type random variables

[摘要] A B S T R A C T 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 L & uuml;roth 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 L & uuml;roth random variables. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-15

[关键词] Oppenheim expansions;Exact weak law;Luroth sequence