Computing the nearest reversible Markov chain
- Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem.
Author: | Adam Nielsen, Marcus Weber |
---|---|
Document Type: | Article |
Parent Title (English): | Numerical Linear Algebra with Applications |
Volume: | 22 |
Issue: | 3 |
First Page: | 483 |
Last Page: | 499 |
Tag: | Convex Optimization; MSM Reversible Markov Chain |
MSC-Classification: | 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY |
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) | |
Year of first publication: | 2015 |
Preprint: | urn:nbn:de:0297-zib-53292 |
DOI: | https://doi.org/10.1002/nla.1967 |