A general bayes rule and its application to nonlinear estimation

This paper consists of two main results, a general Bayes rule, and a general Bucy representation theorem. The general Bayes rule is a natural generalization of the elementary Bayes rule:

$\text{P(A}\text{B)}\text{P(A)}\text{=}\text{P(B}\text{A)}\text{P(B)}$

. The general Bucy representation theorem plays a central role in nonlinear estimation theory as does the Bucy theorem in nonlinear filtering. A simple and direct proof of the general Bucy representation theorem is obtained by the application of the general Bayes rule.