Central limit theorems for martingales-II: convergence in the weak dual topology, with corrections

2023/04/10 by Bruno Rémillard, Bruno N. Remillard, Remillard, Bruno N. +2 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 60G44 #Probability (math.PR) #Secondary 60F17 #Stochastic processes and financial applications #math.PR #msc:60F17 #msc:60G44

paper · pdf · doi:10.48550/arxiv.2304.04887

openalex publication_date 2023/04/10 · openalex created_date 2025/10/10 · arxiv created 2026/07/30 · arxiv updated 2026/07/31 · openalex updated_date 2026/08/02

Abstract

A convergence theorem for martingales with càdlàg trajectories (right continuous with left limits everywhere) is obtained in the sense of the weak dual topology on Hilbert space, under conditions that are much weaker than those required for any of the usual Skorohod topologies. Examples are provided to show that these conditions are also very easy to check and yield useful asymptotic results, especially when the limit is a mixture of stochastic processes with discontinuities.

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