Definition:Filtered Probability Space
Jump to navigation
Jump to search
Definition
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.
Also known as
A filtered probability space may be known as simply a filtered space.