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

Aurélien Garivier (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: perfect simulation; context trees; Markov chains of infinite order; coupling from the past (CFTP); coupling into and from the past (CIAFTP)

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Aurélien Garivier. Perfect Simulation Of Processes With Long Memory: a 'Coupling Into And From The Past' Algorithm. Random Structures and Algorithms, 2015, 46 (2), pp.300-319. ⟨hal-00798388v2⟩