Definition:Stochastic Process/Formal Definition

Definition
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $\struct {E, \mathcal E}$ be a measurable space.

Let $I$ be a set.

Let $\sequence {X_i}_{i \in I}$ be a $I$-indexed family of $E$-valued random variables.

We call $\sequence {X_i}_{i \in I}$ a stochastic process.