Trajectory

Last updated Nov 1, 2022

Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a Probability Space, let $(T, \leq)$ be a Total Ordering, and let $(S, \Sigma)$ be a Measure Space. Let $X: \Omega \to S^{T}$ be a Stochastic Process. Then for $\omega \in \Omega$, $X(\omega)$ is a Trajectory.