Asymptotic inference for stochastic differential equations driven by fractional Brownian motion

Shohei Nakajima*, Yasutaka Shimizu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
JournalJapanese Journal of Statistics and Data Science
DOIs
Publication statusAccepted/In press - 2022

Keywords

  • Fractional Brownian motion
  • Multiplicative noise
  • Parameter estimation
  • Small noise asymptotics
  • Stochastic differential equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Theory and Mathematics

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