Limit theorems for cloning algorithms

Limit theorems for some adaptive MCMC algorithms with subgeometric kernels

Abstract. This paper deals with the ergodicity (convergence of the marginals) and the law of large numbers for adaptive MCMC algorithms built from transition kernels that are not necessarily geometrically ergodic. We develop a number of results that broaden significantly the class of adaptive MCMC algorithms for which rigorous analysis is now possible. As an example, we give a detailed analysis...

Limit theorems for mergesort

Central and local limit theorems (including large deviations) are established for the number of comparisons used by the standard top-down recursive mergesort under the uniform permutation model. The method of proof utilizes Dirichlet series, Mellin transforms and standard analytic methods in probability theory.

Limit Theorems for Bivariate Appell

Consider the stationary linear process X t = P 1 u=?1 a(t?u) u , t 2 Z, where f u g is an i.i.d. nite variance sequence. The spectral density of fX t g may diverge at the origin (long-range dependence) or at any other frequency. Consider now the quadratic form Q N = P N t;s=1 b(t ? s)P m;n (X t ; X s), where P n;m (X t ; X s) denotes a non-linear function (Appell polynomial). We provide general...

Local Limit Theorems for Free

Limit Theorems for toral translations

Toral translations are the simplest dynamical systems. In this talk I will discuss the fluctuations of the number of visits of an orbit of a toral translation to a given set. In particular we discuss how the fluctuations depend on the geometry of the set.