統計数学セミナー

過去の記録 ~08/06次回の予定今後の予定 08/07~

担当者 吉田朋広、荻原哲平、小池祐太
セミナーURL http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/
目的 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う.

2018年05月08日(火)

15:00-16:10   数理科学研究科棟(駒場) 052号室
千葉 航平 氏 (東京大学)
LAN property for stochastic differential equations driven by fractional Brownian motion of Hurst parameter 1/4 < H < 1/2
[ 講演概要 ]
We consider the problem of estimating the drift parameter of solution to the stochastic differential equation driven by a fractional Brownian motion with Hurst parameter less than 1/2 under complete observation. We derive a formula for the likelihood ratio and prove local asymptotic normality when 1/4 < H < 1/2. Our result shows that the convergence rate is $T^{-1/2}$ for the parameters satisfying a certain equation and $T^{-(1-H)}$ for the others.
In this talk, we outline the proof of local asymptotic normality and explain how the different rates of convergence occur and where we use the assumption H > 1/4. We also mention some remaining problems and future directions. This talk is based on arXiv:1804.04108.