Mixingale estimation function for mixed fractional SPDEs with random effect and random sampling

Abstract

We study the mixingale estimation function estimator of the parameters in the fractional stochastic partial differential equation when the process is observed at the arrival times of a Poisson process with the presence of random effect. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we plug-in this estimate in the estimation function to estimate the drift parameter. We obtain the consistency and the asymptotic normality of the mixingale estimation function estimator.