stylistic:style_transfer, information:highlighting
For two stochastic processes

Independence of two stochastic processes is a property between two stochastic processes { X t } t ∈ T {\displaystyle \left\{X_{t}\right\}_{t\in {\mathcal {T}}}} and { Y t } t ∈ T {\displaystyle \left\{Y_{t}\right\}_{t\in {\mathcal {T}}}} that are defined on the same probability space (Ω, F, P) {\displaystyle (\Omega,{\mathcal {F}},P)}. Formally, two stochastic processes { X t } t ∈ T {\displaystyle \left\{X_{t}\right\}_{t\in {\mathcal {T}}}} and { Y t } t ∈ T {\displaystyle \left\{Y_{t}\right\}_{t\in {\mathcal {T}}}} are said to be independent if for all n ∈ N {\displaystyle n\in \mathbb {N} } and for all t 1, …, t n ∈ T {\displaystyle t_{1},\ldots,t_{n}\in {\mathcal {T}}}, the random vectors (X (t 1), …, X (t n)) {\displaystyle (X(t_{1}),\ldots,X(t_{n}))} and (Y (t 1), …, Y (t n)) {\displaystyle (Y(t_{1}),\ldots,Y(t_{n}))} are independent, i.e. if