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. Copyright © 2015 John Wiley & Sons, Ltd.