2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134614In 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 $\frac12<H<\frac3{4}$.14 Pages. To appear in Journal of Theoretical ProbabilityProbability60G15, 60J55, 60H05text