Let X be a bounded adapted right-continuous process, let and define Ui by (16.3) for i ≥ 1. Show each Ui is a stopping time. Let A be a predictable increasing process and let Sk be the kth time A...

Let X be a bounded adapted right-continuous process, let

and define Ui by (16.3) for i ≥ 1. Show each Ui is a stopping time.

Let A be a predictable increasing process and let Sk be the kth time A jumps more than ε. Thus

Show each S_k
is a predictable stopping time.

Show that the stopping times T_n
defined in the proof of Proposition 16.23 are predictable.