On parameter identification in stochastic differential equations by penalized maximum likelihood

Fabian Dunker; Thorsten Hohage

doi:10.1088/0266-5611/30/9/095001

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arXiv · 1404.0651

On parameter identification in stochastic differential equations by penalized maximum likelihood

Fabian Dunker·Thorsten Hohage

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Abstract

In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed operator equation with a deterministic forward operator described by the Fokker-Planck equation. We derive convergence rates of the risk for penalized maximum likelihood estimators with convex penalty terms and for Newton-type methods. The assumptions of our general convergence results are verified for estimation of the drift coefficient. The advantages of log-likelihood compared to quadratic data fidelity terms are demonstrated in Monte-Carlo simulations.

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BibTeX RIS

Fabian Dunker, Thorsten Hohage. 2014-04-02. On parameter identification in stochastic differential equations by penalized maximum likelihood. https://doi.org/10.1088/0266-5611%2F30%2F9%2F095001

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