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On the Linear Fractional Self-attracting Diffusion
Authors:Litan Yan  Yu Sun  Yunsheng Lu
Institution:(1) Department of Mathematics, College of Science, Donghua University, 2999 North Renmin Rd., Songjiang, Shanghai, 201620, People’s Republic of China
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 1/2<H<3/4. The Project-sponsored by NSFC (10571025) and the Key Project of Chinese Ministry of Education (No.106076).
Keywords:Fractional Brownian motion  Self-attracting diffusion  The fractional It? integrals  Local time and self-intersection local time
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