Definition:Filtered Probability Space/Continuous Time

Definition

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

Let $\sequence {\mathcal F_t}_{t \ge 0}$ be a continuous-time filtration of $\Sigma$.

We say that $\struct {\Omega, \Sigma, \sequence {\mathcal F_t}_{t \ge 0}, \Pr}$ is a filtered probability space.

Sources

• 2016: Jean-François Le Gall: Brownian Motion, Martingales, and Stochastic Calculus ... (previous) ... (next): $3.1$: Filtrations and Processes