| AN EXPONENTIAL INEQUALITY FOR AUTOREGRESSIVE PROCESSES IN ADAPTIVE TRACKING |
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| 引用本文： | Bernard BERCU. AN EXPONENTIAL INEQUALITY FOR AUTOREGRESSIVE PROCESSES IN ADAPTIVE TRACKING[J]. 系统科学与复杂性, 2007, 20(2): 243-250. DOI: 10.1007/s11424-007-9021-6 |
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| 作者姓名： | Bernard BERCU |
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| 作者单位： | Institut de Mathematiques de Bordeaux, Universite Bordeaux 1, UMR5251, 351, cours de la liberation, 33405 Talence cedex, France |
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| 基金项目： | This paper is dedicated to Professor Han-Fu Chen for his 70th birthday. |
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| 摘 要： | ![]()
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| 关 键 词： | 自适应跟踪 自回归过程 指数不等式 最小面积 |
| 收稿时间： | 2005-08-09 |
| 修稿时间： | 2007-01-10 |
An Exponential Inequality for Autoregressive Processes in Adaptive Tracking |
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| Bernard Bercu. An Exponential Inequality for Autoregressive Processes in Adaptive Tracking[J]. Journal of Systems Science and Complexity, 2007, 20(2): 243-250. DOI: 10.1007/s11424-007-9021-6 |
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| Authors: | Bernard Bercu |
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| Affiliation: | (1) Institut de Mathematiques de Bordeaux, Universite Bordeaux 1, UMR5251, 351, cours de la liberation, 33405 Talence cedex, France |
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| Abstract: | ![]()
A wide range of literature concerning classical asymptotic properties for linear models with adaptive control is available, such as strong laws of large numbers or central limit theorems. Unfortunately, in contrast with the situation without control, it appears to be impossible to find sharp asymptotic or nonasymptotic properties such as large deviation principles or exponential inequalities. Our purpose is to provide a first step towards that direction by proving a very simple exponential inequality for the standard least squares estimator of the unknown parameter of Gaussian autoregressive process in adaptive tracking. |
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| Keywords: | Adaptive tracking autoregressive process exponential inequalities least squares martingales |
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