| Project/Area Number |
14580344
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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 | The University of Tokyo |
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Principal Investigator |
YOSHIDA Nakahiro The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (90210707)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 2003: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2002: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | partial mixing / asymptotic expansion / Malliavin calculus / stochastic differential equation / filtering / volatility / finance / M-estimation / 条件付き期待値 / マリアヴァン解析 / サンプリング / ザバイバルアナクシス |
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| Research Abstract |
Theory of asymptotic expansions was investigated to develop the statistical inference for stochastic processes.
1. As a generalization of mixing property, the notion of the partial mixing was introduced, and the theory of asymptotic expansion for partial mixing processes was established. This theory was applied to derive expansions for a stochastic regression model with a long-memory explanatory stochastic process. The resulting expansion is not standard in that the second-order term is related with the non-central limit theorem.
2. An extension of the Watanabe theory to a general setting with an abstract Malliavin operator was build, and also conditional expansion formulas were derived as the double Edgeworth expansion. As an application, an algorithm for a filtering problem was provided.
3. We proposed an estimator of the correlation coefficient between two diffusion processes based on non-synchronous observations. This problem was motivated by financial data analysis. Consistency of the estimator was proved.
4. M-estimators of parameters in a stochastic differential equation with jumps were proposed and asymptotic behaviors (consistency, asymptotic normality and asymptotic expansion) were proved.
5. We derived an expansion formula for a stochastic volatility model with the Levy-driven Ornstein-Uhlenbeck process as the volatility term. It enables us to understand the aggregation Gaussianity and non-Gaussianity of the stock returns.
6. We published or prepared paper on asymptotic expansion for epsilon-Markov processes, expansion under degeneracy, and prediction regions.
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