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

TL;DR

This paper establishes a central limit theorem for the $L^3$-modulus of continuity of Brownian local time, advancing understanding of its probabilistic behavior using stochastic analysis techniques.

Contribution

It introduces a novel CLT for the $L^3$-modulus of continuity of Brownian local time, employing asymptotic Knight's theorem and Clark-Ocone formula.

Findings

Proves a CLT for the $L^3$-modulus of continuity of Brownian local time.

Utilizes stochastic analysis tools like Knight's theorem and Clark-Ocone formula.

Provides new insights into the probabilistic structure of Brownian local time.

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.