Parameter estimation of stochastic differential equation driven by small fractional noise. Issue 4 (4th July 2022)

• Record Type: Journal Article
• Authors: Nakajima, Shohei; Shimizu, Yasutaka
• Is Part Of: Statistics. Volume 56:Issue 4(2022)
• Page Start: 919
• Page End: 934
• Publication Date: 2022-07-04
• Subjects: Parameter estimation -- stochastic differential equation -- fractional Brownian motion -- small noise -- asymptotic normality; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2022.2098960
• Languages: English
• ISSNs: 0233-1888

Abstract

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 ∈ ( 0, 1 ) / { 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 ε → 0 .