Statistical asymptotic theory for stochastic processes And its computer implementation
| Project/Area Number |
18500219
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Kobe University (2007-2009)
Hiroshima International University (2006) |
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Principal Investigator |
SAKAMOTO Yuji Kobe University, 人間発達環境学研究科, 准教授 (70215664)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,320,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | 統計的推測 / 時系列解析 / モデル選択 / 数理ファイナンス / 拡散過程 / マーク付き点過程 / 漸近展開 / クレーム過程 / 漸近理論 / 確率過程 / ファイナンス統計 / 点過程 / M推定量 / 裾確率評価 / Wang変換 / キュミュラント推定 |
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| Research Abstract |
The higher-order asymptotic expansions of many test statistics for stochastic processes are obtained, which leads to asymptotic expansion formulas of test statistics for diffusion processes. Highly accurate approximation formulas for major discriminant functions are derived in case of small or ergodic diffusion observations. Moreover, asymptotic expansions of marked point processes with time in-homogenous intensity functions are obtained, and using the mathematical formula manipulation, explicit expression of the coefficients in the expansions are given. Computer program for the approximation formulas obtained are coded, and their accuracy is measured numerically.
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Report
(6 results)
Research Products
(6 results)
