Quasi-likelihood Estimation in Fractional Levy SPDEs from Poisson Sampling

Abstract

We study the quasi-likelihood estimator of the drift parameter in the stochastic partial differential equations driven by a cylindrical fractional Levy process when the process is observed at the arrival times of a Poisson process. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we plug-in this estimate in the quasi-likelihood to estimate the drift parameter. We obtain the strong consistency and the asymptotic normality of the estimators.