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 , 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.
This is the published version, also available here: http://dx.doi.org/10.1214/ECP.v14-1511.
Hu, Yaozhong & Nualart, David. "Stochastic integral representation of the L<sup>2</sup> modulus of Brownian local time and a central limit theorem." (2009) Electronic Communications in Probability. Vol 14, pp. 1-10. http://dx.doi.org/10.1214/ECP.v14-1511.
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