Markovian Maximal Coupling of Markov Processes

2017/10/26 by Björn Böttcher, Böttcher, Björn · 1 citation
Mathematics · #60G05 #60J25 #60J35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1710.09654

openalex publication_date 2017/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Markovian maximal couplings of Markov processes are characterized by an equality of total variation and a distance of Wasserstein type. If a Markovian maximal coupling is a Feller process, the generator can be calculated, e.g. for reflection coupled Brownian motion. Apart from processes with continuous paths also jump processes are treated for the first time. For subordinated Brownian motion a Markovian maximal coupling is constructed by subordinating reflection coupled Brownian motion. This coupling is the unique Markovian maximal coupling and its generator is determined by state-space dependent mirror coupling of the corresponding Lévy measures.

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