Parameter estimation of stochastic differential equation driven by small fractional noise

Abstract

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with the Hurst index $H\in (0,1)/\{\frac{1}{2}\}$. Under some assumptions on the drift coefficient, we obtain the asymptotic normality and moment convergence of maximum likelihood estimator of the drift parameter when a small dispersion coefficient $\epsilon \to 0$.

Keywords:

• Parameter estimation
• stochastic differential equation
• fractional Brownian motion
• small noise
• asymptotic normality

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The second author was partially supported by JSPS KAKENHI [grant number JP21K03358] and Japan Science and Technology Agency (JST) CREST [grant number JPMJCR14D7], Japan.