統計数学セミナー

過去の記録 ~04/13次回の予定今後の予定 04/14~

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.

2007年12月12日(水)

15:20-16:30   数理科学研究科棟(駒場) 122号室
Stefano IACUS 氏 (Department of Economics, Business and Statistics, University of Milan)
Inference problems for the telegraph process observed at discrete times
[ 講演概要 ]
The telegraph process {X(t), t>0}, has been introduced (see
Goldstein, 1951) as an alternative model to the Brownian motion B(t).
This process describes a motion of a particle on the real line which
alternates its velocity, at Poissonian times, from +v to -v. The
density of the distribution of the position of the particle at time t
solves the hyperbolic differential equation called telegraph equation
and hence the name of the process.
Contrary to B(t) the process X(t) has finite variation and
continuous and differentiable paths. At the same time it is
mathematically challenging to handle. Several variation of this
process have been recently introduced in the context of Finance.

In this talk we will discuss pseudo-likelihood and moment type
estimators of the intensity of the Poisson process, from discrete
time observations of standard telegraph process X(t). We also
discuss the problem of change point estimation for the intensity of
the underlying Poisson process and show the performance of this
estimator on real data.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/12.html