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

D. T. Crommelin, E. Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)782-805
Number of pages24
JournalJournal of Computational Physics
Issue number2
StatePublished - Sep 20 2006


  • Embedding problem
  • Inverse problems
  • Markov chains
  • Timeseries analysis

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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