Abstract
Let (Xn) ∞ n=0 denote a Markov chain on a Polish space that has a stationary distribution ω. This article concerns upper bounds on the Wasserstein distance between the distribution of Xn and ω. In particular, an explicit geometric bound on the distance to stationarity is derived using generalized drift and contraction conditions whose parameters vary across the state space. These new types of drift and contraction allow for sharper convergence bounds than the standard versions, whose parameters are constant. Application of the result is illustrated in the context of a non-linear autoregressive process and a Gibbs algorithm for a random effects model.
Original language | English (US) |
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Pages (from-to) | 872-889 |
Number of pages | 18 |
Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |
Volume | 58 |
Issue number | 2 |
DOIs | |
State | Published - May 2022 |
Bibliographical note
Funding Information:The second author was supported by NSF Grant DMS-15-11945.
Publisher Copyright:
© 2022 Institute of Mathematical Statistics. All rights reserved.
Keywords
- Convergence analysis
- Exponential convergence
- Kantorovich-Rubinstein distance
- Lyapunov drift function
- Polish space
- Quantitative bound