Remarks on drift estimation for diffusion processes

Yvo Pokern, Andrew M. Stuart, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


In applications such as molecular dynamics it is of interest to fit Smoluchowski and Langevin equations to data. Practitioners often achieve this by a variety of seemingly ad hoc procedures such as fitting to the empirical measure generated by the data and fitting to properties of autocorrelation functions. Statisticians, on the other hand, often use estimation procedures, which fit diffusion processes to data by applying the maximum likelihood principle to the path-space density of the desired model equations, and through knowledge of the properties of quadratic variation. In this paper we show that the procedures used by practitioners and statisticians to fit drift functions are, in fact, closely related and can be thought of as two alternative ways to regularize the (singular) likelihood function for the drift. We also present the results of numerical experiments which probe the relative efficacy of the two approaches to model identification and compare them with other methods such as the minimum distance estimator.

Original languageEnglish (US)
Pages (from-to)69-95
Number of pages27
JournalMultiscale Modeling and Simulation
Issue number1
StatePublished - 2009


  • Diffusion process
  • Langevin equation
  • Maximum likelihood principle
  • Minimum distance estimator
  • Molecular dynamics
  • Nonparametric estimation
  • Parameter estimation
  • Reversible diffusion process

ASJC Scopus subject areas

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


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