A Central Limit Theorem for Iterated Random Functions

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...

My title

For a martingale (Xn) converging almost surely to a random variable X , the sequence (Xn − X) is called martingale tail sum. Recently, Neininger [Random Structures Algorithms, 46 (2015), 346-361] proved a central limit theorem for the martingale tail sum of Régnier’s martingale for the path length in random binary search trees. Grübel and Kabluchko [2014, preprint, arXiv 1410.0469] gave an alte...

A central limit theorem and law of the iterated logarithm for a random field with exponential decay of correlations

In [6], Walter Philipp wrote that “. . . the law of the iterated logarithm holds for any process for which the Borel-Cantelli Lemma, the central limit theorem with a reasonably good remainder and a certain maximal inequality are valid.” Many authors [1, 2, 4, 5, 9] have followed this plan in proving the law of the iterated logarithm for sequences (or fields) of dependent random variables. We ca...