TY - JOUR
T1 - Asymptotic inference for stochastic differential equations driven by fractional Brownian motion
AU - Nakajima, Shohei
AU - Shimizu, Yasutaka
N1 - Funding Information:
The second author was partially supported by JSPS KAKENHI Grant Numbers JP21K03358 and JST CREST JPMJCR14D7, Japan.
Publisher Copyright:
© 2022, The Author(s) under exclusive licence to Japanese Federation of Statistical Science Associations.
PY - 2022
Y1 - 2022
N2 - We study a problem of parametric estimation for continuously observed stochastic processes involving fractional Brownian motion with Hurst index H∈ (1 / 2 , 1). Under some assumptions on the drift and volatility coefficients, we obtain the asymptotic normality and moment convergence of maximum likelihood type estimator of the drift parameter under the small noise asymptotics such that the driving noise vanishes.
AB - We study a problem of parametric estimation for continuously observed stochastic processes involving fractional Brownian motion with Hurst index H∈ (1 / 2 , 1). Under some assumptions on the drift and volatility coefficients, we obtain the asymptotic normality and moment convergence of maximum likelihood type estimator of the drift parameter under the small noise asymptotics such that the driving noise vanishes.
KW - Fractional Brownian motion
KW - Multiplicative noise
KW - Parameter estimation
KW - Small noise asymptotics
KW - Stochastic differential equation
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U2 - 10.1007/s42081-022-00181-z
DO - 10.1007/s42081-022-00181-z
M3 - Article
AN - SCOPUS:85140406842
JO - Japanese Journal of Statistics and Data Science
JF - Japanese Journal of Statistics and Data Science
SN - 2520-8764
ER -