State Space

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 ${X_{t}: \Omega \to S}_{t \in T}$ be a Stochastic Process. Then $S$ is referred to as the State Space.