Donsker-Varadhan Type Large Deviation Principles for U-statistics
| Project/Area Number |
10640113
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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 | Kanazawa University |
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Principal Investigator |
NAKAGAWA Shuya Kanazawa University, Faculty of Engineering, Professor, 工学部, 教授 (50185899)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1999: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1998: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | large deviation / U-statistics / V-statistics / stochastic differential equation / Euler-Maruyama scheme / Brownina motion / 大域偏差理論 / ノンパラメトリック統計 |
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| Research Abstract |
The investigator investigated large deviation principles for symmetric statistics using new technique which is an application of limit theorems for Banach space valued i.i.d. random variables. Usually well known Hoeffding decomposition for symmetric scholastics cannot be used for symmetric statistics with non-degenerate kernels. He solved by the method to obtain Donsker-Varadhan type large deviation principles.
The numerical solution of Ito's stochastic differential equation (SDE) is realized by pseudo-random numbers which are defined by some algebraic algorithms in terms of an approximate solution on computers. Since any algorithm has an essential defect for independence and distribution, as Knuth (1981) pointed out. The investigator focused on the distribution of pseudo-random numbers and consider the error estimation of the Euler-Maruyama approximation when the distribution of underlying random variables is different from the normal distribution.
One of important problems in stochastic analysis is to consider stochastic differential equations with boudary conditions on multi-dimensional domains (so-called Skorohod SDE). There are two approaches to define approximate solutions of such stochastic differential equations. Saisho (1987) constructed Skorohod equations using the projection on the boundary. Roughly speaking, the reflecting path is defined for given function by the following manner : Define a step function by discretization of the Brownian motion and construct the reflecting step function for the Brownian motion. The investigator define Euler-Maruyama type approximate solutions of it using penalty method and investigate the rate of convergence.
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Report
(3 results)
Research Products
(13 results)
