Conditions for Sample-Continuity and the Central Limit Theorem

Martingales, Lévy’s continuity theorem, and the martingale central limit theorem

Central Limit Theorem and Almost Sure Central Limit Theorem for the Product of Some Partial Sums

Let (Xn)n≥1 be a sequence of independent identically distributed (i.i.d.) positive random variables (r.v.). Recently there have been several studies to the products of partial sums. It is well known that the products of i.i.d. positive, square integrable random variables are asymptotically log-normal. This fact is an immediate consequence of the classical central limit theorem (CLT). This point...

Almost Sure Central Limit Theorem of Sample Quantiles

Copyright q 2012 Yu Miao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We obtain the almost sure central limit theorem ASCLT of sample quantiles. Furthermore, based on the method, the ASCLT of order statistics is also pro...

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

A Functional Central Limit Theorem for The

In this paper, we present a functional fluid limit theorem and a functional central limit theorem for a queue with an infinity of servers M/GI/∞. The system is represented by a point-measure valued process keeping track of the remaining processing times of the customers in service. The convergence in law of a sequence of such processes after rescaling is proved by compactness-uniqueness methods...