What Is the Integral Formulation of the Chapman-Kolmogorov Formula?

[eljose]

Hello..where i could find information about the Chapmann-Kolmogorov formula for continuous probability..i have hear something when taking a course of QM...something about this...if you want to go from A point to B point with a certain probability crossing a point C then:

$$P(A,B)=P(A,C)P(B,C)$$

My question is what is the Integral or differential formulation of this law?..considering we know all the probability distributions..thanks.

 

[iStealth]

the Chapman-Kolmogorov equation
$$p(\mathbf{x}_{k}|\mathbf{z}_{1:k-1})= \int<br /> p(\mathbf{x}_{k}|\mathbf{x}_{k-1})p(\mathbf{x}_{k-1}|\mathbf{z}_{1:k-1})d\mathbf{x}_{k-1}$$as an example, from "A Tutorial on Particle Filters for On-line Non-linear/Non-Gaussian Bayesian Tracking (2001)"