Parameter estimations for linear parabolic fractional SPDEs with jumps

Abstract

We give an unbiased and consistent estimator for the drift coefficient of a linear parabolic stochastic partial differential equation driven by a multiplicative cylindrical fractional Brownian motion with Hurst index $1/2 <h < 1$ and a cylindrical centered Poisson process, if the observations of the solution process are given in discrete time points. The presented method is based on mean square estimations.