Central limit theorems for martingales-I : continuous limits
Probability
2024-01-22 v3
Abstract
When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient conditions for both processes to be independent. Examples of applications are provided, notably for occupation time processes and statistical estimators of financial volatility measures.
Cite
@article{arxiv.2301.07267,
title = {Central limit theorems for martingales-I : continuous limits},
author = {Bruno Rémillard and Jean Vaillancourt},
journal= {arXiv preprint arXiv:2301.07267},
year = {2024}
}