On parameter identification in stochastic differential equations by penalized maximum likelihood

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.

References in corpus (4)

• Penalized nonparametric mean square estimation of the coefficients of diffusion processes
• Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data
• Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data
• Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression

Cited by in corpus (3)

• Verification of a variational source condition for acoustic inverse medium scattering problems
• On the asymptotical regularization for linear inverse problems in presence of white noise
• Nonparametric Estimation of the Random Coefficients Model in Python