Finding dominant structures of nonreversible Markov processes. A SIAM Interdisciplinary Journal

N. Djurdjevac Conrad, M. Weber, Ch. Schütte – 2016

Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g., for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or a mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral-based methods for reversible processes by using Schur decomposition techniques which can also tackle nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments.

Titel
Finding dominant structures of nonreversible Markov processes. A SIAM Interdisciplinary Journal
Verfasser
N. Djurdjevac Conrad, M. Weber, Ch. Schütte
Datum
2016
Kennung
10.1137/15M1032272
Zitierweise
A SIAM Interdisciplinary Journal, 2016, 14 (4), 1319-1340
Art
Text
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