In the field of automatic control, systems with stochastic inputs are frequently encountered. The purpose of this paper is twofold: (I) to treat the problem of mathematically modelling a general class of stochastic systems, and (2) to simulate the optimal control for a special case of this class of stochastic systems, specifically a linear time-invariant system with stochastic inputs and stochastically perturbed observations. The general class of systems considered in the modelling includes systems having non-linear and time-varying state dependence and additive white noise which is added in a non-linear and time-varying manner.