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arXiv · 0707.2627

On the linear fractional self-attracting diffusion

Litan Yan·Yu Sun·Yunsheng Lu
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Abstract

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized self-intersection local time exists in L^2 if $\frac12<H<\frac3{4}$.

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Litan Yan, Yu Sun, Yunsheng Lu. 2007-07-18. On the linear fractional self-attracting diffusion. https://arxiv.org/abs/0707.2627

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