Central Limit Theorem for Deterministic Systems

CENTRAL LIMIT THEOREM FOR DETERMINISTIC SYSTEMSCarlangelo

A uniied approach to obtaining the central limit theorem for hyperbolic dynamical systems is presented. It builds on previous results for one dimensional maps but it applies to the multidimensional case as well.

Central and Local Limit Theories in Markov Dependent 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.

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Central Limit Theorems and Diffusion Approximations for Multiscale Markov Chain Models1 by Hye-won Kang,

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple timescales, by a combination of the two. Motivated by models with multiple timescales arising in systems biology, we present a general approach to proving a central limit theorem cap...

M ar 2 00 1 Limit theorems for the painting of graphs by clusters ∗

Abstract We consider a generalization of the so-called divide and color model recently introduced by Häggström . We investigate the behaviour of the magnetization in large boxes and its fluctuations. Thus, laws of large numbers and Central Limit theorems are proved, both quenched and annealed. We show that the properties of the underlying percolation process roughly influence the behaviour of t...