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### Remarks on drift estimation for diffusion processes

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Pokern, Yvo, Stuart, A. M. and Vanden-Eijnden, Eric.
(2009)
*Remarks on drift estimation for diffusion processes.*
Multiscale Modeling & Simulation, Vol.8
(No.1).
pp. 69-95.
ISSN 1540-3459

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Official URL: http://dx.doi.org/10.1137/070694806

## Abstract

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

auto-correlation 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 note we show that these 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.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science > Mathematics |

Library of Congress Subject Headings (LCSH): | Diffusion processes, Langevin equations, Parameter estimation, Molecular dynamics |

Journal or Publication Title: | Multiscale Modeling & Simulation |

Publisher: | World Scientific Publishing Co. Pte. Ltd. |

ISSN: | 1540-3459 |

Official Date: | 2009 |

Volume: | Vol.8 |

Number: | No.1 |

Number of Pages: | 27 |

Page Range: | pp. 69-95 |

Identification Number: | 10.1137/070694806 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

References: | [1] F. M. Bandi and P. C. B. Phillips, Fully nonparametric estimation of scalar diffusion models, |

URI: | http://wrap.warwick.ac.uk/id/eprint/3058 |

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