The measurability of hitting times

TL;DR

This paper presents a new, simplified proof that under broad conditions, the hitting time of a set by a stochastic process is a stopping time, with implications for optional and predictable set theorems.

Contribution

It provides a novel, straightforward proof of the measurability of hitting times, enhancing understanding of stochastic process properties.

Findings

Hitting times are stopping times under general conditions

Section theorems follow easily from the proof

Simplifies understanding of optional and predictable sets

Abstract

Under very general conditions the hitting time of a set by a stochastic process is a stopping time. We give a new simple proof of this fact. The section theorems for optional and predictable sets are easy corollaries of the proof.