Abstract
Let be a weighted-fractional Brownian motion with Hurst indexes a and b such that and In this paper, we consider the linear self-repelling diffusion with where are two real parameters. The process is an analogue of the linear self-interacting diffusion (Cranston and Le Jan, Math. Ann. 303 (1995), 87-93). We introduce its large time behaviors, and the behavior presents a recursive convergence which is quite different from the asymptotic behavior of stochastic differential equations without interacting drifts. As a related question, we also consider the asymptotic behaviors of the least squares estimations of θ and ν.