LAN property for stochastic differential equations driven by fractional Brownian motion of Hurst parameter $H\in (1/4,1/2)$

Abstract

In this paper, we consider the problem of estimating the drift parameter of solution to the stochastic differential equation driven by a fractional Brownian motion with Hurst parameter less than $1/2$ under complete observation. We derive a formula for the likelihood ratio and prove local asymptotic normality when $H\in (1/4,1/2)$. Our result shows that the convergence rate is $T^{-1/2}$ for the parameters satisfying a certain equation and $T^{-(1-H)}$ for the others.

arXiv commentv1: 48 pages, comments are welcome. v2: 48 pages, (1) some proofs are simplified, (2) some mistakes are corrected, and (3) a sketch of the proof and the calculation of the Fisher information in fOU case are added

References in corpus (4)

• Random attractors for a class of stochastic partial differential equations driven by general additive noise
• Approximation of stationary solutions of Gaussian driven Stochastic Differential Equations
• Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion
• LAN property for stochastic differential equations with additive fractional noise and continuous time observation