QUANTITATIVE COARSE-GRAINING OF MARKOV CHAINS
(2024) In SIAM Journal on Mathematical Analysis 56(1). p.913-954- Abstract
Coarse-graining techniques play a central role in reducing the complexity of stochastic models and are typically characterized by a mapping which projects the full state of the system onto a smaller set of variables which captures the essential features of the system. Starting with a continuous-time Markov chain, in this work we propose and analyze an effective dynamics, which approximates the dynamical information in the coarse-grained chain. Without assuming explicit scale-separation, we provide sufficient conditions under which this effective dynamics stays close to the original system and provide quantitative bounds on the approximation error. We also compare the effective dynamics and corresponding error bounds to the averaging... (More)
Coarse-graining techniques play a central role in reducing the complexity of stochastic models and are typically characterized by a mapping which projects the full state of the system onto a smaller set of variables which captures the essential features of the system. Starting with a continuous-time Markov chain, in this work we propose and analyze an effective dynamics, which approximates the dynamical information in the coarse-grained chain. Without assuming explicit scale-separation, we provide sufficient conditions under which this effective dynamics stays close to the original system and provide quantitative bounds on the approximation error. We also compare the effective dynamics and corresponding error bounds to the averaging literature on Markov chains which involve explicit scale-separation. We demonstrate our findings on an illustrative test example.
(Less)
- author
- Hilder, Bastian LU and Sharma, Upanshu
- organization
- publishing date
- 2024
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- coarse-graining, continuous-time Markov chains, effective dynamics, functional inequalities, relative entropy, slow-fast system
- in
- SIAM Journal on Mathematical Analysis
- volume
- 56
- issue
- 1
- pages
- 42 pages
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- scopus:85183732434
- ISSN
- 0036-1410
- DOI
- 10.1137/22M1473996
- language
- English
- LU publication?
- yes
- id
- 55b5ddfc-8ef2-4fb8-8449-b9240e1ac69b
- date added to LUP
- 2024-02-27 14:42:50
- date last changed
- 2024-02-27 14:44:34
@article{55b5ddfc-8ef2-4fb8-8449-b9240e1ac69b,
abstract = {{<p>Coarse-graining techniques play a central role in reducing the complexity of stochastic models and are typically characterized by a mapping which projects the full state of the system onto a smaller set of variables which captures the essential features of the system. Starting with a continuous-time Markov chain, in this work we propose and analyze an effective dynamics, which approximates the dynamical information in the coarse-grained chain. Without assuming explicit scale-separation, we provide sufficient conditions under which this effective dynamics stays close to the original system and provide quantitative bounds on the approximation error. We also compare the effective dynamics and corresponding error bounds to the averaging literature on Markov chains which involve explicit scale-separation. We demonstrate our findings on an illustrative test example.</p>}},
author = {{Hilder, Bastian and Sharma, Upanshu}},
issn = {{0036-1410}},
keywords = {{coarse-graining; continuous-time Markov chains; effective dynamics; functional inequalities; relative entropy; slow-fast system}},
language = {{eng}},
number = {{1}},
pages = {{913--954}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM Journal on Mathematical Analysis}},
title = {{QUANTITATIVE COARSE-GRAINING OF MARKOV CHAINS}},
url = {{http://dx.doi.org/10.1137/22M1473996}},
doi = {{10.1137/22M1473996}},
volume = {{56}},
year = {{2024}},
}