2015/03/31 by Agnès Coquio, Agnes Coquio, Coquio, Agnes
Computer Science · Mathematics · #Algorithms and Data Compression #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference #math.PR
paper · pdf · doi:10.48550/arxiv.1503.09165
arxiv created 2015/03/31 · openalex publication_date 2015/03/31 · arxiv updated 2015/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An aperiodic and irreducible Markov chain on a finite state space converges to its stationary distribution. When convergence to equilibrium is measured by total variation distance, there exists an optimal coupling and a maximal coupling time. In this article, the maximal coupling time is compared to the hitting time of a specific state or set. Such sets, named halting sets, are studied in the case of symmetric birth-and-death chains and in some other examples. Some applications to the cutoff phenomenon are given. These results yield new methods to calculate cutoff times for some monotone birth-and death chains without the lazy hypothesis .