Properties of Brownian Motion One denotes the Brownian motion by where in general , and the following properties hold:
a.Given , ,,…., are mutually independent and . Such a process has independent moments.
b.For any , , depends only on and not . Which means the process has stationary increments, Figure 6.4.
Figure 6.4: A hypothetical example of a stationary process with respect to variance
where in general 
, and the following properties hold:
, 
,
,…., 
are mutually independent 
and 
. 
, 
, 
depends only on 
and not 
. Which means the process has stationary increments, Figure 6.4.
