Title: Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models,
Abstract: This paper deals with the estimation problem of misspecified ergodic Lévy
driven stochastic differential equation models based on high-frequency samples.
We utilize the widely applicable and tractable Gaussian quasi-likelihood
approach which focuses on (conditional) mean and variance structure. It is
shown that the corresponding Gaussian quasi-likelihood estimators of drift and
scale parameters satisfy tail probability estimates and asymptotic normality at
the same rate as correctly specified case. In this process, extended Poisson
equation for time-homogeneous Feller Markov processes plays an important role
to handle misspecification effect. Our result confirms the practical usefulness
of the Gaussian quasi-likelihood approach for SDE models, more firmly.