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

Abstract

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.

Authors:
 [1];  [2]
  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 (United States). E-mail: crommelin@cims.nyu.edu
  2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 (United States). E-mail: eve2@cims.nyu.edu
Publication Date:
OSTI Identifier:
20840351
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 217; Journal 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)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MARKOV PROCESS; MINIMIZATION; MOLECULAR DYNAMICS METHOD; PROBABILITY; PROGRAMMING; SIMULATION

Citation Formats

Crommelin, D.T., and Vanden-Eijnden, E. Fitting timeseries by continuous-time Markov chains: A quadratic programming approach. United States: N. p., 2006. Web. doi:10.1016/j.jcp.2006.01.045.
Crommelin, D.T., & Vanden-Eijnden, E. Fitting timeseries by continuous-time Markov chains: A quadratic programming approach. United States. doi:10.1016/j.jcp.2006.01.045.
Crommelin, D.T., and Vanden-Eijnden, E. 2006. "Fitting timeseries by continuous-time Markov chains: A quadratic programming approach". United States. doi:10.1016/j.jcp.2006.01.045.
@article{osti_20840351,
title = {Fitting timeseries by continuous-time Markov chains: A quadratic programming approach},
author = {Crommelin, D.T. and Vanden-Eijnden, E.},
abstractNote = {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.},
doi = {10.1016/j.jcp.2006.01.045},
journal = {Journal of Computational Physics},
number = 2,
volume = 217,
place = {United States},
year = 2006,
month = 9
}
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