On parameter identification in stochastic differential equations by penalized maximum likelihood

Fabian Dunker () and 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.

Date: 2014-04
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Published in Inverse Problems, 2014, 30, 095001

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