Sigma-algebra

Stopping time sigma-algebras

A stopping time${\displaystyle \tau }$ can define a ${\displaystyle \sigma }$-algebra ${\displaystyle {\mathcal {F}}_{\tau },}$ the so-called stopping time sigma-algebra, which in a filtered probability space describes the information up to the random time ${\displaystyle \tau }$ in the sense that, if the filtered probability space is interpreted as a random experiment, the maximum information that can be found out about the experiment from arbitrarily often repeating it until the time ${\displaystyle \tau }$ is ${\displaystyle {\mathcal {F}}_{\tau }.}$