Moments can only be defined for real-valued functions of random variables (or complex-valued, etc.
What is Random Variable in Statistics?In probability, a real-valued function, defined over the sample space of a random experiment, is called a random variable.
Independence of two stochastic processes is a property between two stochastic processes
{
X
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}
t
T
{\displaystyle \left\{X_{t}\right\}_{t\in {\mathcal {T}}}}
and
{
Y
}
t
T
{\displaystyle \left\{Y_{t}\right\}_{t\in {\mathcal {T}}}}
that are defined on the same probability space
(
,
F
,
P
)
{\displaystyle (\Omega ,{\mathcal {F}},P)}
. .