How can you use a Stochastic Differential Equation

From: james (jimwatson1111_at_hotmail.com)
Date: 02/10/05 

Date: 9 Feb 05 19:31:03 -0500 (EST)

Hello

I have a question. If you have a stochastic Differential Equation, and
you can determine a analitical solution for it. What does This
actually mean or how can I use it.

If, for example with a stochastic linear ODE could I determine the
probablity ofthe finial value being in a certain set in state space.Eg
using indicator functions.
 
Can I take expectations of the finial answer and interpret things

My mathematical background isn't too strong but I have heard of the
kalman filter. How could this fit into this framework.