The purpose of this note is to prove a central limit theorem for the third integrated moment of the Brownian local time increments 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 third integrated moment of the Brownian local time increments.
This is the published version, also available here: http://dx.doi.org/10.1214/ECP.v15-1573.
Hu, Yaozhong & Nualart, David. "Central limit theorem for the third moment in space of the Brownian local time increments." (2010) Electronic Communications in Probability. Vol 15. pp. 396 - 410. http://dx.doi.org/10.1214/ECP.v15-1573.
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