Minimal elements of stopping time $\sigma$-algebras

TL;DR

The paper characterizes minimal elements of stopping time sigma-algebras using the minimal elements of the underlying filtration's sigma-algebra, providing clearer intuition and an illustrative example.

Contribution

It offers a new way to understand stopping time sigma-algebras through minimal elements, enhancing interpretability.

Findings

Minimal elements of stopping time sigma-algebras are expressed via those of the underlying filtration.

Provides an intuitive interpretation of stopping time sigma-algebras.

Includes an illustrative example to demonstrate the concepts.

Abstract

We show how minimal elements of a stopping time $\sigma$-algebra can be expressed in terms of the minimal elements of the $\sigma$-algebra of the underlying filtration. This facilitates an intuitive interpretation of stopping time $\sigma$-algebras. An example is provided.