ABSTRACT
Stochastic calculus extends classical differential and integral calculus to functions with a random component arising from indeterminacy or system noise. The fundamental construct is the Ito integral, whose description and analysis, as well as an explication of it's role in solving stochastic differential equations (SDEs), are the main goals of this chapter. The principal tool used in determining the solution of an SDE is the Ito-Doeblin formula, a generalization of the chain rule of Newtonian calculus. To put the theory in perspective, we begin with a brief discussion of classical differential equations.
