Note on Martingale Theory and Applications
Machine Learning
2026-02-16 v3 Artificial Intelligence
Probability
Abstract
This note investigates core properties of martingales, emphasizing the measure-theoretic formulation of conditional expectation, the martingale transform, and the upcrossing lemma. These results lead to the Martingale Convergence Theorem, which we then apply to study the extinction behavior in Galton--Watson branching processes.
Cite
@article{arxiv.2602.05774,
title = {Note on Martingale Theory and Applications},
author = {Xiandong Zou},
journal= {arXiv preprint arXiv:2602.05774},
year = {2026}
}