The maximum likelihood type estimator of SDEs with fractional Brownian motion under small noise asymptotics in the rough case (2406.07804v3)

Abstract: We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood estimator and establish its the asymptotic normality and moment convergence of the drift parameter when a small dispersion coefficient vanishes.