Optimal control problem by using Ito calculus

Abstract

In this research were discussed stochastic differential equation and how to solve it. Where we studied the theory of measurement and integration, and explain concept of a random variable and its relation to the function of measurable how to change measure the integration. And then studied the Brownian motion and the most important properties and not to the possibility of integration by Lebesgue integrating. To solve the stochastic differential equation we used ITO integral after studying this integration and its properties. It also contains research on applications of stochastic differential equation and the most important issue of control random.