## 統計数学セミナー

担当者 吉田朋広、増田弘毅、荻原哲平、小池祐太 http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/ 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.

### 2010年03月15日(月)

14:00-15:00   数理科学研究科棟(駒場) 002号室
Alexandre Brouste 氏 (Université du Maine)
Statistical inference in the partial observation setting, in continuous time
[ 講演概要 ]
In various fields, the {\\it signal} process, whose law depends on an unknown parameter $artheta \\in \\Theta \\subset \\R^p$, can not be observed directly but only through an {\\it observation} process. We will talk about the so called fractional partial observation setting, where the observation process $Y=\\left( Y_t, t \\geq 0 ight)$ is given by a stochastic differential equation: egin{equation} \\label{mod:modelgeneral} Y_t = Y_0 + \\int_0^t h(X_s, artheta) ds + \\sigma W^H_t\\,, \\quad t > 0 \ where the function $h: \\, \\R imes \\Theta \\longrightarrow \\R$ and the constant $\\sigma>0$ are known and the noise $\\left( W^H_t\\,, t\\geq 0 ight)$ is a fractional Brownian motion valued in $\\R$ independent of the signal process $X$ and the initial condition $Y_0$. In this setting, the estimation of the unknown parameter $artheta \\in \\Theta$ given the observation of the continuous sample path $Y^T=\\left( Y_t , 0 \\leq t \\leq T ight)$, $T>0$, naturally arises.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html