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

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

2009-08-18

arxiv.org/abs/0908.2473v1

Mathematics

Probability

Scientific paper

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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