2012 Fiscal Year Final Research Report
Statistical inference for stochastic differential equations from discrete observation and its applications
| Project/Area Number |
21540126
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University |
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Principal Investigator |
UCHIDA Masayuki 大阪大学, 大学院・基礎工学研究科, 教授 (70280526)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 高頻度データ / 確率方程式 / 最尤型推定量 / 大偏差不等式 |
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| Research Abstract |
We considered statistically asymptotic inference for volatility parameters of stochastic differential equations from high frequency data observed on the fixed interval. By using the polynomial type large deviation inequality for the statistical random field, we showed the asymptotic mixed normality of maximum likelihood type estimator and Bayes type estimator of the volatility parameter and the moments of convergences of the estimators. Under nh^p ->0, where h is the discretization step size, n is the sample size and p is an integer value greater than 2, adaptive maximum likelihood estimators of both drift and volatility parameters for discretely observed ergodic diffusion processes were obtained, and their asymptotic normality and moment convergence wereproved. Moreover, we treated adaptive estimators of drift and volatility parameters for misspecified ergodic diffusion processes from discrete observations and their asymptotic properties were shown.
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