| |
Kolmogorov Equations
As usual let us again consider  as the Markov process in continuous time and continuous state set up such that the following assumptions are considered to be true:
 , 
 , where  is the drift coefficient.
 , where  is the diffusion coefficient.
Then the corresponding forward Kolmorogov equation and backward Kolmorogov equation are given by:
Note
- In case
 then the Markov process is homogeneous and we have  and  , i.e., both are independent of time  .
- If the Markov process is additive, then
 depends only on  and  and not on  , hence  and we have  and  , i.e., both are independent of time  .
|
