Stochastic integral representation of the $L^{2}$ modulus of Brownian local time and a central limit theorem

Yaozhong Hu; David Nualart

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arXiv · 0908.2473

Stochastic integral representation of the $L^{2}$ modulus of Brownian local time and a central limit theorem

Yaozhong Hu·David Nualart

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Abstract

The purpose of this note is to prove a central limit theorem for the $L^2$-modulus of continuity of the Brownian local time obtained in \cite{CLMR}, 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 $L^2$-modulus of the Brownian local time.

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BibTeX RIS

Yaozhong Hu, David Nualart. 2009-08-18. Stochastic integral representation of the $L^{2}$ modulus of Brownian local time and a central limit theorem. https://arxiv.org/abs/0908.2473

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