A note on faithful coupling of Markov chains

10/27/2017
by   Debojyoti Dey, et al.
0

One often needs to turn a coupling (X_i, Y_i)_i≥ 0 of a Markov chain into a sticky coupling where once X_T = Y_T at some T, then from then on, at each subsequent time step T'≥ T, we shall have X_T' = Y_T'. However, not all of what are considered couplings in literature, even Markovian couplings, can be turned into sticky couplings, as proved by Rosenthal through a counter example. Rosenthal then proposed a strengthening of the Markovian coupling notion, termed as faithful coupling, from which a sticky coupling can indeed be obtained. We identify the reason why a sticky coupling could not be obtained in the counter example of Rosenthal, which motivates us to define a type of coupling which can obviously be turned into a sticky coupling. We show then that the new type of coupling that we define, and the faithful coupling as defined by Rosenthal, are actually identical. Our note may be seen as a demonstration of the naturalness of the notion of faithful coupling.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/24/2020

The Coupling/Minorization/Drift Approach to Markov Chain Convergence Rates

This review paper provides an introduction of Markov chains and their co...
research
05/04/2021

Continuous indetermination and average likelihood minimization

The authors transpose a discrete notion of indetermination coupling in t...
research
09/07/2023

Evaluating Microservice Organizational Coupling based on Cross-service Contribution

For traditional modular software systems, "high cohesion, low coupling" ...
research
08/05/2019

On the Relationship Between Coupling and Refactoring: An Empirical Viewpoint

[Background] Refactoring has matured over the past twenty years to becom...
research
11/20/2022

Learning Nonlinear Couplings in Network of Agents from a Single Sample Trajectory

We consider a class of stochastic dynamical networks whose governing dyn...
research
12/12/2019

Variational Coupling Revisited: Simpler Models, Theoretical Connections, and Novel Applications

Variational models with coupling terms are becoming increasingly popular...
research
04/20/2021

Computing Arlequin coupling coefficient for concurrent FE-MD approaches

Arlequin coupling coefficient is essential for concurrent FE-MD models w...

Please sign up or login with your details

Forgot password? Click here to reset