Module 3:Branching process, Application of Markov chains, Markov Processes with discrete and continuous state space
Lecture 12:Weiner Process
In order to find the differential equations of Weiner process we are interestd to find the infinitesimal shift in the particle's position as time progresses. Assume the probabilities of and are independent of and . Then using Taylor series expansion we have:
Here we consider
Thus:
(3.10)
We also know that
(3.11)
Using (3.9), (3.10) and (3.11) and after some simplification along with the fact that , we obtain
and 
are 
and 
. Then using Taylor series expansion we have:
, 
we obtain
