Perfect Simulation Of Processes With Long Memory: A `Coupling Into And From The Past' Algorithm

TL;DR

This paper introduces a novel perfect simulation algorithm for variable length Markov chains and systems with perfect connections, enhancing convergence speed and relaxing kernel conditions, applicable across various fields.

Contribution

It generalizes existing perfect simulation methods by incorporating coupling into and from the past, improving efficiency and applicability for complex stochastic processes.

Findings

Accelerates convergence in perfect simulation algorithms.

Relaxes conditions on the transition kernel for broader applicability.

Effective for chains of variable or infinite order.

Abstract

We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling into and from the past. It improves on existing algorithms by relaxing the conditions on the kernel and by accelerating convergence, even in the simple case of finite order Markov chains. Although chains of variable or infinite order have been widely investigated for decades, their use in applied probability, from information theory to bio-informatics and linguistics, has recently led to considerable renewed interest.