Identification of a time-dependent control parameter for a stochastic diffusion equation

In this paper, we are interested in a time-dependent control parameter identification for a stochastic diffusion equation. First, we analyze the ill-posedness of the inverse problem by deriving the regularities of the solution to the direct problem in the sense of expectation. With the first moment of the realizations of average data in some sub-domain, we prove the existence and uniqueness of the identification problem. Then, the mollification regularization method is taken to regularize the inverse problem and the a prior convergence rate of the regularized solution is derived. Next, an inversion algorithm which can be paralleled is proposed to solve this inverse problem. Several numerical experiments are presented to show the efficiency of the inversion algorithm.