Various discrete-time representations of a class of stochastic distributed parameter systems for optimal state estimator design are proposed and their properties are examined. Four different types of discrete-time models are considered: the first is an exact model by means of Green's function technique and the other three are approximate models by forward-, backward- and forward-averaging-differences in time. It is found that the forward-difference approximation leads to an unstable discrete-time model while the remaining three preserve the stability of the original distributed parameter systems. In addition, unlike the lumped-parameter systems, the state estimator based on the discrete-time model derived from forward-difference is proven to be unstable. An illustrative numerical example for a simple diffusion process is given.