Stochastic Differential Equation

Consider . Moreover partition the interval  into  and define , where .

Now by Rieman Integral we know that , where . Moreover .

Using the fundamentals mentioned above we can easily obtain the following which is  and also define

Its Calculus

Without any loss of generality assume  and define  where  is the standard Brownian motion.

Furthermore we may write .

Using some calculation we can show that the BS model differential equations is