Stochastic integral representation of the L² modulus of Brownian local time and a central limit theorem

2009/08/18 by Yaozhong Hu, David Nualart, Hu, Yaozhong +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0908.2473

openalex publication_date 2009/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this note is to prove a central limit theorem for the L²-modulus of continuity of the Brownian local time obtained in \citeCLMR, using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic version of Knight's theorem and the Clark-Ocone formula for the L²-modulus of the Brownian local time.

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