Category:Definitions/Filtered Probability Spaces

This category contains definitions related to Filtered Probability Spaces.
Related results can be found in Category:Filtered Probability Spaces.

Discrete Time

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

Let $\sequence {\mathcal F_n}_{n \mathop \in \N}$ be a discrete-time filtration of $\Sigma$.

We say that $\struct {\Omega, \Sigma, \sequence {\mathcal F_n}_{n \mathop \in \N}, \Pr}$ is a filtered probability space.

Continuous Time

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.