Category:Stopped Processes
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This category contains results about stopped processes.
Let $\struct {\Omega, \Sigma, \sequence {\FF_n}_{n \ge 0}, \Pr}$ be a filtered probability space.
Let $\sequence {X_n}_{n \ge 0}$ be an $\sequence {\FF_n}_{n \ge 0}$-adapted stochastic process.
Let $T$ be a stopping time with respect to $\sequence {\FF_n}_{n \ge 0}$.
We define the stopped process $\sequence {X_n^T}_{n \ge 0}$ by:
- $\map {X_n^T} \omega = \map {X_{\map T \omega \wedge n} } \omega$
for each $\omega \in \Omega$, where $\wedge$ is the pointwise minimum.
We write:
- $X_n^T = X_{T \wedge n}$
Subcategories
This category has the following 3 subcategories, out of 3 total.
Pages in category "Stopped Processes"
The following 4 pages are in this category, out of 4 total.