Question

Give a general condition on a map $\phi: \mathbb{R} \rightarrow \mathbb{R}$ such that $\phi(T)$ is a stopping time for any stopping time $T$.

   Give a general condition on a map $\phi: \mathbb{R} \rightarrow \mathbb{R}$ such that $\phi(T)$ is a stopping time for any stopping time $T$.

Stochastic Calculus and Applications

Stochastic Calculus and Applications

Samuel N. Cohen,… 1st Edition

Chapter 3, Problem 12

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** A stopping time $T$ with respect to a filtration $(\mathcal{F}_t)_{t \geq 0}$ is a random variable taking values in $[0, \infty]$ such that for every $t \geq 0$, the event $\{T \leq t\}$ is in the $\sigma$-algebra $\mathcal{F}_t$. This means that the decision to Show more…

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Give a general condition on a map $\phi: \mathbb{R} \rightarrow \mathbb{R}$ such that $\phi(T)$ is a stopping time for any stopping time $T$.

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