Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.15779 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929523184893952 |
|---|---|
| author | Kim, Jin Won Taghvaei, Amirhossein Mehta, Prashant G. |
| author_facet | Kim, Jin Won Taghvaei, Amirhossein Mehta, Prashant G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15779 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Divergence metrics in the study of Markov and hidden Markov processes Kim, Jin Won Taghvaei, Amirhossein Mehta, Prashant G. Probability 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. |
| title | Divergence metrics in the study of Markov and hidden Markov processes |
| topic | Probability |
| url | https://arxiv.org/abs/2404.15779 |