Central limit theorem for the modulus of continuity of the Brownian local time in $L^3(\mathbb{R})$

Yaozhong Hu; David Nualart

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arXiv · 0912.2400

Central limit theorem for the modulus of continuity of the Brownian local time in $L^3(\mathbb{R})$

Yaozhong Hu·David Nualart

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Abstract

The purpose of this note is to prove a central limit theorem for the $L^3$-modulus of continuity of the Brownian local time 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 $L^3$-modulus of the Brownian local time.

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Yaozhong Hu, David Nualart. 2009-12-12. Central limit theorem for the modulus of continuity of the Brownian local time in $L^3(\mathbb{R})$. https://arxiv.org/abs/0912.2400

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