• Corpus ID: 249240227

Order estimate of functionals related to fractional Brownian motion and asymptotic expansion of the quadratic variation of fractional stochastic differential equation

@inproceedings{Yamagishi2022OrderEO,
  title={Order estimate of functionals related to fractional Brownian motion and asymptotic expansion of the quadratic variation of fractional stochastic differential equation},
  author={Hayate Yamagishi and Nakahiro Yoshida},
  year={2022}
}
We derive an asymptotic expansion for the quadratic variation of a stochastic process satisfying a stochastic differential equation driven by a fractional Brownian motion, based on the theory of asymptotic expansion of Skorohod integrals converging to a mixed normal limit. In order to apply the general theory, it is necessary to estimate functionals that are a randomly weighted sum of products of multiple integrals of the fractional Brownian motion, in expanding the quadratic variation and… 

Asymptotic expansion of an estimator for the Hurst coefficient

Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. For this, a recently developed theory of asymptotic expansion of the distribution of