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Complete Convergence and Complete Moment Convergence for Martingale Diference Sequence 被引量:8
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作者 Xue Jun WANG Shu He HU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第1期119-132,共14页
In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type The... In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for martingale diference sequence.As an application,a strong law of large numbers for martingale diference sequence is obtained. 展开更多
关键词 martingale diference sequence complete convergence complete moment convergence Baum–Katz-type theorem
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Performance analysis of stochastic gradient algorithms under weak conditions 被引量:14
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作者 DING Feng YANG HuiZhong LIU Fei 《Science in China(Series F)》 2008年第9期1269-1280,共12页
By using the stochastic martingale theory, convergence properties of stochastic gradient (SG) identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the S... By using the stochastic martingale theory, convergence properties of stochastic gradient (SG) identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the SG algorithms consistently converge to the true parameters, as long as the information vector is persistently exciting (i.e., the data product moment matrix has a bounded condition number) and that the process noises are zero mean and uncorrelated. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist, and the processes are stationary and ergodic and the strong persis- tent excitation condition holds. This contribution greatly relaxes the convergence conditions of stochastic gradient algorithms. The simulation results with bounded and unbounded noise variances confirm the convergence conclusions proposed. 展开更多
关键词 recursive identification parameter estimation least squares stochastic gradient multivariable systems convergence properties martingale convergence theorem
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