Adapted Process

Last updated Nov 1, 2022

Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a Probability Space. Let $X: \Omega \to S^{T}$ be a Stochastic Process with State Space $(S, \Sigma)$, and let $\mathcal{F} := (\mathcal{B}{t}){t \in T}$ be a Filtration on $\Omega$. Then we say $X$ is adapted to $\mathcal{F}$ if $X_{t}$ is $(\mathcal{B}_{t}, \Sigma)$-measureable.