Practical drift conditions for subgeometric rates of convergence

Randal Douc (1, 2) , Gersende Fort (3, 2) , Éric Moulines (2) , Philippe Soulier (4)

1 CMAP - Centre de Mathématiques Appliquées
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 SELECT - Model selection in statistical learning
4 MODAL'X - Modélisation aléatoire de Paris X

We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a \psi-irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by Jarner and Roberts [Ann. Appl. Probab. 12 (2002) 224-247] for polynomial convergence rates, turns out to be very convenient to prove subgeometric rates of convergence. Several applications are presented including nonlinear autoregressive models, stochastic unit root models and multidimensional random walk Hastings-Metropolis algorithms.

Mots clés: Markov chains; stationary distribution; rate of convergence

Domaines: Probabilités [math.PR]

Randal Douc, Gersende Fort, Éric Moulines, Philippe Soulier. Practical drift conditions for subgeometric rates of convergence. The Annals of Applied Probability, 2004, 14 (3), pp.1353-1377. ⟨10.1214/105051604000000323⟩. ⟨hal-00147616⟩