structural:expansion
Continuous-time white noise

Such a process is said to be white noise in the strongest sense if the value w (t) {\displaystyle w(t)} for any time t {\displaystyle t} is a random variable that is statistically independent of its entire history before t {\displaystyle t}. A weaker definition requires independence only between the values w (t 1) {\displaystyle w(t_{1})} and w (t 2) {\displaystyle w(t_{2})} at every pair of distinct times t 1 {\displaystyle t_{1}} and t 2 {\displaystyle t_{2}}. An even weaker definition requires only that such pairs w (t 1) {\displaystyle w(t_{1})} and w (t 2) {\displaystyle w(t_{2})} be uncorrelated. As in the discrete case, some authors adopt the weaker definition for "white noise", and use the qualifier independent to refer to either of the stronger definitions. Others use weakly white and strongly white to distinguish between them.