Definition:Right-Continuous Filtration of Sigma-Algebra

Definition

Let $\struct {X, \Sigma}$ be a measurable space.

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

We say that $\sequence {\FF_t}_{t \ge 0}$ is right-continuous if and only if for each $t \in \hointr 0 \infty$, we have:

$\FF_{t^+} = \FF_t$

where $\FF_{t^+}$ is the right-limit of $\sequence {\FF_t}_{t \ge 0}$ at $t$.

Sources

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