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arXiv · 2308.10889

On the radius of self-repellent fractional Brownian motion

Le Chen·Sefika Kuzgun·Carl Mueller·Panqiu Xia
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Abstract

We study the radius $R_T$ of a self-repellent fractional Brownian motion $\left\{B^H_t\right\}_{0\le t\le T}$ taking values in $\mathbb{R}^d$. Our sharpest result is for $d=1$, where we find that with high probability, \begin{equation*} R_T \asymp T^ν, \quad \text{with $ν=\frac{2}{3}\left(1+H\right)$.} \end{equation*} For $d>1$, we provide upper and lower bounds for the exponent $ν$, but these bounds do not match.

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Le Chen, Sefika Kuzgun, Carl Mueller, Panqiu Xia. 2023-11-28. On the radius of self-repellent fractional Brownian motion. https://arxiv.org/abs/2308.10889

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