Definition

Let $\eta,\tau$ be stopping times. We define the stochastic interval as $$<span class="wikilink-unresolved" title="Note not published">\eta,\tau</span>=\{ (t,\omega)\in\mathbb{R}^{+}\times\Omega: \eta(\omega)\le t \le \tau(\omega) \}$$ ## Note For $0\le s<t$, $$<span class="wikilink-unresolved" title="Note not published">s,t</span>=[s,t]\times\Omega$$