A Simple Proof of the Bichteler-Dellacherie Theorem

TL;DR

This paper provides an elementary proof of the Bichteler-Dellacherie-Mokobodzki Theorem, establishing that a process is a good integrator if and only if it is a semimartingale, with implications for classical Riemann integrability.

Contribution

It offers a simplified, accessible proof of a fundamental theorem linking good integrators and semimartingales, enhancing understanding of stochastic integration.

Findings

Elementary proof of the Bichteler-Dellacherie-Mokobodzki Theorem

Characterization of semimartingales via Riemann integrability

Clarification of conditions for processes to be good integrators

Abstract

We give a simple and rather elementary proof of the celebrated Bichteler-Dellacherie-Mokobodzki Theorem, which states that a process S is a good integrator if and only if it is a semimartingale. As a corollary, we obtain a characterization of semimartingales along the lines of classical Riemann integrability.