On parameter identification in stochastic differential equations by penalized maximum likelihood

摘要

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