Practical drift conditions for subgeometric rates of convergence

By Randal Douc, Gersende Fort, Eric Moulines, Philippe Soulier. 2004

189 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/12bca861fe862914dc36caa4f608dac4cd63a244

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In Statistics and Probability

Citations in the corpus

SUBGEOMETRIC ERGODICITY OF STRONG MARKOV PROCESSES (2005, methodology): “This compromise between the rate function and the norm of convergence is well known for the discrete parameter Markov chain ([35]; see also [4, 8, 14]).”
On the Markov chain central limit theorem (2004, background): “Several m otivating exam ples are given which range from toy one-dim ensionalsettings to com plicated settingsencountered in M arkov chain M onte Carlo.”
Regenerative block bootstrap for Markov chains (2006, background): “In particular, it is well known that 'block' moment conditions may be replaced by drift criteria of Lyapunov's type; see Chapter 11 in Meyn and Tweedie (1996) for further details on such conditions and many examples, as well as Doue et al. (2004) for recent results.”
Subgeometric rates of convergence of Markov processes in the Wasserstein metric (2012, background): “We establish subgeometric bounds on the convergence rate, thus generalizing the results of [4, 5, 11].”
Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (2012, background): “[12]), whereas Corollary 27(b) implies polynomial rates of convergence (cf.”
Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, background): “It should be mentioned that subgeometric ergodicity of Markov processes has been studied by many others authors in various settings; see [8, 17, 24, 34, 43, 50, 58, 59] and the references therein.”
Markov chain Monte Carlo: Can we trust the third significant figure? (2007, background): “…(1999), Rosenthal (1995, 1996), Roy and Hobert (2007) and Tierney (1994) examined Gibbs samplers while Christensen, Moller and Waagepetersen (2001), Douc et al. (2004), Fort and Moulines (2000, 2003), Geyer (1999), Jarner and Hansen (2000), Jarner and Roberts (2002), Meyn and Tweedie (1994) and…”