On the linear fractional self-attracting diffusion

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Yan, Litan
Sun, Yu
Lu, Yunsheng
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Abstract
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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 $\frac12<H<\frac3{4}$.
Comment: 14 Pages. To appear in Journal of Theoretical Probability
Keywords
Mathematics - Probability, 60G15, 60J55, 60H05
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