Definition:Right-Limit of Filtration of Sigma-Algebra
Jump to navigation
Jump to search
Definition
Let $\struct {X, \Sigma}$ be a measurable space.
Let $\sequence {\FF_t}_{t \ge 0}$ be a continuous-time filtration of $\Sigma$.
For each $t \in \hointr 0 \infty$ we define the right-limit at $t$, $\FF_{t+}$ by:
- $\ds \FF_{t+} = \bigcap_{s > t} \FF_s$
Also see
Sources
- 2016: Jean-François Le Gall: Brownian Motion, Martingales, and Stochastic Calculus ... (previous) ... (next): $3.1$: Filtrations and Processes