Open Access
September 2006 Reconstruction of diffusions using spectral data from timeseries
Daan Crommelin, Eric Vanden-Eijnden
Commun. Math. Sci. 4(3): 651-668 (September 2006).


A numerical technique for the reconstruction of diffusion processes (diffusions, in short) from data is presented. The drift and diffusion coeffcients of the generator of the diffusion are found by minimizing an object function which measures the difference between the eigenspectrum of the operator and a reference eigenspectrum. The reference spectrum can be obtained, in discretized form, from time-series through the construction of a discrete-time Markov chain. Discretization of the Fokker-Planck operator turns minimization of the object function into a quadratic programming problem on a convex domain, for which well-established solution methods exist. The technique is a generalization of a reconstruction procedure for continuous-time Markov chain generators, recently developed by the authors. The technique also allows us to derive the coeffcients in the homogenized diffusion for the slow variables in systems with multiple timescales.


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Daan Crommelin. Eric Vanden-Eijnden. "Reconstruction of diffusions using spectral data from timeseries." Commun. Math. Sci. 4 (3) 651 - 668, September 2006.


Published: September 2006
First available in Project Euclid: 5 April 2007

MathSciNet: MR2247935

Primary: 60J60
Secondary: 60H10 , 60H35 , 62G05 , 62M10 , 62M15

Keywords: Diffusions , Parameter estimation , Stochastic differential equations

Rights: Copyright © 2006 International Press of Boston

Vol.4 • No. 3 • September 2006
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