## Seminar on Probability and Statistics

Organizer(s) Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike

### 2010/03/15

14:00-15:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Alexandre Brouste (Université du Maine)
Statistical inference in the partial observation setting, in continuous time
[ Abstract ]
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.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html