Existence and Uniqueness Solution of an Optimal Control Problem Via Stochastic Differential Equation

This paper deal with the existence and uniqueness solutions of an optimal control problem using stochastic differential equations, the important properties and the solutions of such equations. A particular consequence is the connection with the classic partial differential equation (PDE) methods for studying diffusions, the Kolmogorov forward (Fokker-Planck) and backward equations. Where the Stochastic Differential Equations (SDE) is considered as an ordinary differential equations (ODE) driven by white noise we justified the connection between the Ito’s integral and white noise in the case of non-random integrands (interpreted as test functions). The sequence of ODEs, driven by approximations to white noise limiting to an SDE which is very important in the stochastic modelling of physical systems and simulation of SDE on a computer was also considered