Two-step estimation of ergodic Lévy driven SDE

We consider high frequency samples from ergodic Lévy driven stochastic differential equation with drift coefficient a(x, α) and scale coefficient c(x, γ) involving unknown parameters α and γ. We suppose that the Lévy measure ν₀, has all order moments but is not fully specified. We will prove the joint asymptotic normality of some estimators of α, γ and a class of functional parameter ∫ φ(z) ν₀(dz) , which are constructed in a two-step manner: first, we use the Gaussian quasi-likelihood for estimation of (α, γ) ; and then, for estimating ∫ φ(z) ν₀(dz) we make use of the method of moments based on the Euler-type residual with the the previously obtained quasi-likelihood estimator.