Given a probability space $(\Omega\,\mathcal{F},P)$ and a measurable space $(\mathbb{R}^n, \mathcal{B}(\mathbb{R}^n)) ,$ an $\mathbb{R}^n$-valued stochastic process is a collection of $\mathbb{R}^n$-valued random variables on $\Omega$ , indexed by a totally ordered set $\{ t|t\ge0 \}$