Quasi-likelihood and Quasi-Bayes Estimation in Noncommutative Fractional SPDEs

Abstract

We study the quasi-likelihood and quasi Bayes estimator of the drift parameter in the stochastic partial differential equations when the process is observed at the arrival times of a Poisson process. Unlike the previous work, no commutativity condition is assumed between the operators in the equation. 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. Under certain non-degeneracy assumptions on the operators, we obtain the consistency and the asymptotic normality of the estimators.