Stopped process
In mathematics, a stopped process is a stochastic process that is forced to assume the same value after a prescribed (possibly random) time. == Definition == Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} )} be a probability space; ( X , A ) {\displaystyle (\mathbb {X} ,{\mathcal {A}})} be a measurable space; X : [ 0 , + ∞ ) × Ω → X {\displaystyle X:[0,+\infty )\times \Omega \to \mathbb {X} } be a stochastic process; τ : Ω → [ 0 , + ∞ ] {\displaystyle \tau :\Omega \to [0,+\infty ]} be a stopping time with respect to some filtration { F t | t ≥ 0 } {\displaystyle \{{\mathcal {F}}_{t}|t\geq 0\}} of F {\displaystyle {}{\mathcal {F}}} .