Measuring the "non-stopping timeness" of ends of previsible sets

TL;DR

This paper introduces new methods to quantify how much the ends of previsible sets deviate from being stopping times, with analysis of explicit examples involving martingale last passage times.

Contribution

It proposes several measurements for non-stopping timeness of ends of previsible sets and studies explicit examples involving martingale last passage times.

Findings

New measurements for non-stopping timeness introduced

Explicit examples involving martingale last passage times analyzed

Provides insights into the structure of previsible set ends

Abstract

In this paper, we propose several "measurements" of the "non-stopping timeness" of ends g of previsible sets, such that g avoids stopping times, in an ambiant filtration. We then study several explicit examples, involving last passage times of some remarkable martingales.