Asymptotic behavior of the linear self-interacting diffusions with a weight

Let$B^H=\{B^H_t,t\geq0\}$be a fractional Brownian motion with Hurst index$H\in(0,1)$.

In this talk, we consider long time behaviors of the self-interacting diffusions of the form

$$X^H_t=B^H_t+\int_0^t\int_0^sg(r)dX_rds+\nut,$$

where$g$is a Borel measurable function. Moreover, when the function$g$includes some parameters we introduce the least squares estimators of these parameters and consider their asymptotic behaviors.