Parameter estimate for a linear parabolic fractional SPDE with jumps

A drift parameter estimation problem is studied for a linear parabolic stochastic partial differential equation driven by a multiplicative cylindrical fractional Brownian motion with Hurst index h ∈]1/2, 1[ and a multiplicative Poisson process with values in a Hilbert space. Equations are introduced for the Galerkin approximations of the mild solution process. A mean square estimation criterion is used for these equations. It is proved that the estimate is unbiased and weakly consistent for the original problem.