Divergence metrics in the study of Markov and hidden Markov processes
Abstract
This paper is divided into two parts. The first part reviews the formulae for f-divergences in the study of continuous-time Markov processes and explores their applications in areas such as stochastic stability, the second law of thermodynamics, and its non-equilibrium extensions. This sets the foundation for the second part, which focuses on f-divergence in the study of hidden Markov processes. In this context, we present analyses of filter stability and stochastic thermodynamics, with the latter being used to illustrate the concept of a Maxwell demon in an over-damped Langevin model with white noise observations. The paper's expository style and unified formalism for both Markov and hidden Markov processes aim to serve as a valuable resource for researchers working across related fields.
Keywords
Cite
@article{arxiv.2404.15779,
title = {Divergence metrics in the study of Markov and hidden Markov processes},
author = {Jin Won Kim and Amirhossein Taghvaei and Prashant G. Mehta},
journal= {arXiv preprint arXiv:2404.15779},
year = {2024}
}