Two stochastic processes^{} $\{X(t)\mid t\in T\}$ and
$\{Y(t)\mid t\in T\}$ are said to be
if for any positive integer $$, and any
sequence ${t}_{1},\mathrm{\dots},{t}_{n}\in T$, the random vectors
$\bm{X}:=(X({t}_{1}),\mathrm{\dots},X({t}_{n}))$ and
$\bm{Y}:=(Y({t}_{1}),\mathrm{\dots},Y({t}_{n}))$ are independent^{}. This means,
for any two $n$dimensional Borel sets $A,B\subseteq {\mathbb{R}}^{n}$,
we have

$$P\left[{\bm{X}}^{1}(A)\cap {\bm{Y}}^{1}(B)\right]=P\left[{\bm{X}}^{1}(A)\right]P\left[{\bm{Y}}^{1}(B)\right].$$ 
