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統計数学セミナー
過去の記録 ～04/23｜次回の予定｜今後の予定 04/24～
| 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. |
2009年04月15日(水)
15:00-16:10 数理科学研究科棟(駒場) 128号室
Jean JACOD 氏 (Universite Paris VI)
A survey on realized p-variations for semimartingales
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
Jean JACOD 氏 (Universite Paris VI)
A survey on realized p-variations for semimartingales
[ 講演概要 ]
Let $X$ be a process which is observed at the times $i\\Delta_n$ for $i=0,1,\\ldots,$. If $p>0$ the realized $p$-variation over the time interval $[0, t]$ is
V^n(p)_t=\\sum_{i=1}^{[t/\\Delta_n]}|X_{i\\Delta_n}-X_{(i-1)\\Delta_n}|^p.
The behavior of these $p$-variations when $\\Delta_n ightarrow 0$ (and t is fixed) is now well understood, from the point of view of limits in probability (these are basically old results due to Lepingle) and also for the associated central limit theorem.
The aim of this talk is to review those results, as well as a few extensions (multipower variations, truncated variations). We will put some emphasis on the assumptions on $X$ which are needed, depending on the value of $p$.
[ 参考URL ]Let $X$ be a process which is observed at the times $i\\Delta_n$ for $i=0,1,\\ldots,$. If $p>0$ the realized $p$-variation over the time interval $[0, t]$ is
V^n(p)_t=\\sum_{i=1}^{[t/\\Delta_n]}|X_{i\\Delta_n}-X_{(i-1)\\Delta_n}|^p.
The behavior of these $p$-variations when $\\Delta_n ightarrow 0$ (and t is fixed) is now well understood, from the point of view of limits in probability (these are basically old results due to Lepingle) and also for the associated central limit theorem.
The aim of this talk is to review those results, as well as a few extensions (multipower variations, truncated variations). We will put some emphasis on the assumptions on $X$ which are needed, depending on the value of $p$.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
