130 - Moment Equations: Itô Calculus

Abstract

This chapter describes the yield and application of Itô calculus. It is applicable to a set of stochastic differential equations. It yields a system of ordinary differential equations from which different moments may be determined. Using Itô calculus, a set of ordinary differential equations may be determined that will describe the moments of a random process. In the Itô calculus, there are two different types of differential elements. There are dt terms, which are small; and there are dβ terms (Brownian motion terms), which are random. Brownian motion is the integral of white noise when n(s) is white noise. This relation is different from the result in the classical calculus by the inclusion of the last term. This relationship may be used to determine moment equations for a random process.