Stochastic Differential Equations
摘要
In this chapter, we will give a very general review to the main results in the subject of stochastic differential equation (SDE), which are important in stochastic filtering theory. We will start from the theory of stochastic integral, which serves to be a foundation in the development of SDEs. The famous Itô’s formula and Girsanov’s change-of-measure method, as well as the Burkholder-Davis-Gundy inequality, are presented here and will be applied in the derivation of filtering equations in Chap. 5 .