Central limit theorem for semi-markov random evolutions

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

Central Limit Theorem for Random Fields

A new variant of CLT is established for random elds de ned on Rd which are strictly stationary, with nite second moment and weakly dependent (comprising cases of positive or negative association). The summation domains grow in the van Hove sense. Simultaneously the indices of observations form more and more dense grids in these domains. Thus the e ect of combining two scaling procedures is stud...

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...

On the Markov chain central limit theorem

The goal of this paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov chains. This is done with a view towards Markov chain Monte Carlo settings and hence the focus is on the connections between drift and mixing conditions and their implications. In particular, we consider three commonly cited central limit theorems and discuss th...