Null controllability for stochastic semi-discrete parabolic equations

In this paper, we present a null controllability result for a class of stochastic semi-discrete parabolic equations. For this purpose, an observability estimate is established for backward stochastic semi-discrete parabolic equations, with an explicit observability constant that depends on the discretization parameter. This estimate is obtained by a new Carleman estimate for backward stochastic semi-discrete parabolic operators.