2015/10/13 by Timo Hirscher, Hirscher, Timo, Anders Martinsson +1
Economics, Econometrics and Finance · Mathematics · #60C05 #60J10 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60C05 #msc:60J10
paper · pdf · doi:10.48550/arxiv.1510.03661
openalex publication_date 2015/10/13 · arxiv created 2017/02/14 · arxiv updated 2017/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dealing with finite Markov chains in discrete time, the focus often lies on convergence behavior and one tries to make different copies of the chain meet as fast as possible and then stick together. There is, however, a very peculiar kind of discrete finite Markov chain, for which two copies started in different states can be coupled to meet almost surely in finite time, yet their distributions keep a total variation distance bounded away from 0, even in the limit as time goes off to infinity. We show that the supremum of total variation distance kept in this context is \frac12.