Text only print
Full screen print
Seminar on Probability and Statistics
Seminar information archive ～05/20｜Next seminar｜Future seminars 05/21～
| 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
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html
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 arthetainThetasubsetRp, 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(Yt,tgeq0ight) 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 \\end{equation} where the function h:,RimesThetalongrightarrowR and the constant sigma>0 are known and the noise left(WHt,,tgeq0ight) is a fractional Brownian motion valued in R independent of the signal process X and the initial condition Y0. In this setting, the estimation of the unknown parameter arthetainTheta given the observation of the continuous sample path YT=left(Yt,0leqtleqTight), T>0, naturally arises.
[ Reference URL ]In various fields, the {\\it signal} process, whose law depends on an unknown parameter arthetainThetasubsetRp, 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(Yt,tgeq0ight) 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 \\end{equation} where the function h:,RimesThetalongrightarrowR and the constant sigma>0 are known and the noise left(WHt,,tgeq0ight) is a fractional Brownian motion valued in R independent of the signal process X and the initial condition Y0. In this setting, the estimation of the unknown parameter arthetainTheta given the observation of the continuous sample path YT=left(Yt,0leqtleqTight), T>0, naturally arises.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html
