Fitting timeseries by continuous-time Markov chains: A quadratic programming approach

Journal Article · Wed Sep 20 00:00:00 EDT 2006 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2006.01.045· OSTI ID:20840351

Crommelin, D T ^[1]; Vanden-Eijnden, E ^[1]

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1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 (United States)

Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows.

• OSTI ID: 20840351
• Journal Information: Journal of Computational Physics, Vol. 217, Issue 2; Other Information: DOI: 10.1016/j.jcp.2006.01.045; PII: S0021-9991(06)00040-4; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MARKOV PROCESS
MINIMIZATION
MOLECULAR DYNAMICS METHOD
PROBABILITY
PROGRAMMING
SIMULATION