On a backward problem for multidimensional Ginzburg-Landau equation with random data

In this paper, we consider a backward in time problem for the Ginzburg Landau equation in a multidimensional domain associated with some random data. The problem is ill-posed in the sense of Hadamard. To regularize the instable solution, we develop a new regularized method combined with statistical approach. We prove an upper bound on the rate of convergence of the mean integrated squared error in L² and H¹ norms.