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arXiv · 0910.2922

A stochastic calculus proof of the CLT for the L^{2} modulus of continuity of local time

Jay Rosen
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Abstract

We give a stochastic calculus proof of the Central Limit Theorem \[ {\int (L^{x+h}_{t}- L^{x}_{t})^{2} dx- 4ht\over h^{3/2}} \stackrel{\mathcal{L}}{\Longrightarrow}c(\int (L^{x}_{t})^{2} dx)^{1/2} η\] as $h\to 0$ for Brownian local time $L^{x}_{t}$. Here $η$ is an independent normal random variable with mean zero and variance one.

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Jay Rosen. 2009-10-15. A stochastic calculus proof of the CLT for the L^{2} modulus of continuity of local time. https://arxiv.org/abs/0910.2922

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