Local Limit Theorems for Gibbs{markov Maps

Central and Local Limit Theories in Markov Dependent Random Variables

Geometric Ergodicity and Hybrid Markov Chains

Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will “inherit” the geometric ergo...

Geometric Ergodicity of Gibbs Samplers

Due to a demand for reliable methods for exploring intractable probability distributions, the popularity of Markov chain Monte Carlo (MCMC) techniques continues to grow. In any MCMC analysis, the convergence rate of the associated Markov chain is of practical and theoretical importance. A geometrically ergodic chain converges to its target distribution at a geometric rate. In this dissertation,...

A Local Limit Theorem for Stationary Processes in the Domain of Attraction of a Normal Distribution

We prove local limit theorems for Gibbs-Markov processes in the domain of attraction of normal distributions. x1 Introduction It is well known that a random variable X belongs to the domain of attraction of a normal distribution DA(2) if its characteristic function satisses () log E exppitX] = itt ? 1 2 t 2 L(1=jtj) for some slowly varying function L : R + ! R + which is bounded below and some ...

Thermodynamic limit for large random trees

We consider Gibbs distributions on finite random plane trees with bounded branching. We show that as the order of the tree grows to infinity, the distribution of any finite neighborhood of the root of the tree converges to a limit. We compute the limiting distribution explicitly and study its properties. We introduce an infinite random tree consistent with these limiting distributions and show ...