A general framework for perfect simulation of long memory processes

TL;DR

This paper introduces a generalized framework for perfect simulation of stationary processes with long memory, extending previous methods by defining backward coalescence times to operate under weaker conditions.

Contribution

It generalizes existing perfect simulation techniques for long memory processes by introducing backward coalescence times, enabling broader applicability.

Findings

Successfully constructs perfect simulation algorithms under weaker conditions.

Extends the theoretical foundation for simulating long memory processes.

Provides a unified framework for perfect simulation of countable state space processes.

Abstract

In this paper a general approach for the perfect simulation of a stationary process with at most countable state space is outlined. The process is specified through a kernel, prescribing the probability of each state conditional to the whole past history. We follow the seminal paper of Comets, Fernandez and Ferrari, where sufficient conditions for the construction of a certain perfect simulation algorithm have been given. We generalize this approach by defining backward coalescence times for these kind of processes; this allows us to construct perfect simulation algorithms under weaker conditions.