Central limit theorems for martingales-I : continuous limits

Bruno Rémillard; Jean Vaillancourt

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arXiv · 2301.07267

Central limit theorems for martingales-I : continuous limits

Bruno Rémillard·Jean Vaillancourt

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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.

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Bruno Rémillard, Jean Vaillancourt. 2023-01-18. Central limit theorems for martingales-I : continuous limits. https://arxiv.org/abs/2301.07267

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