Remainder term estimates in a conditional central limit theorem for integer-valued random variables

Central Limit Theorem for Banach Space Valued Fuzzy Random Variables

In this paper we prove a central limit theorem for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.

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.

Central and Local Limit Theories in Markov Dependent Random Variables

A Central Limit Theorem for Integer Partitions

Abstract. Recently, Hwang proved a central limit theorem for restricted Λ-partitions, where Λ can be any nondecreasing sequence of integers tending to infinity that satisfies certain technical conditions. In particular, one of these conditions is that the associated Dirichlet series has only a single pole on the abscissa of convergence. In the present paper, we show that this condition can be r...

A Central Limit Theorem for Random Fields

A central limit theorem is proved for α-mixing random fields. The sets of locations where the random field is observed become more and more dense in an increasing sequence of domains. The central limit theorem concerns these observations. The limit theorem is applied to obtain asymptotic normality of kernel type density estimators. It turns out that in our setting the covariance structure of th...