• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1013-1015
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• 2005

Liu[Fuzzy Optimization and Decision Making, 2(2003), 87-100] proved that convergence in credibility does not imply convergence a.s. and convergence in mean does not imply convergence a.s. by giving counter-examples. But these examples are not true. In this note, we prove that convergence in credibility implies convergence a.s. and convergence in mean implies convergence a.s.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.357-366
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• 2016

In this paper, deferred statistical convergence is defined by using deferred $Ces{\grave{a}}ro$ mean instead of $Ces{\grave{a}}ro$ mean in the definition of statistical convergence. The obtained method is compared with strong deferred $Ces{\grave{a}}ro$ mean and statistical convergence under some certain assumptions. Also, some inclusion theorems and examples are given.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.621-640
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• 2022

The aim of this study is to establish some mean convergence theorems for double array of fuzzy random variables in metric space endowed with a convex combination operation under various assumptions.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.435-441
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• 1999

A 'convergence in probability' rate of the empirical distributions and quantiles of linear processes is obtained. As an application of the limit theorems, a trimmed mean for the location of the linear process is considered. It is shown that the trimmed mean is asymptotically normal. A consistent estimator for the asymptotic variance of the trimmed mean is provided.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.8
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• pp.616-625
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• 2002

In this paper, we drove the filtered-x least mean fourth (FXLMF) algorithm where the error raised to the power of four is minimized and analyzed its convergence behavior for a multiple sinusoidal acoustic noise and Gaussian measurement noise. The application of the FXLMF adaptive filter to active noise control requires to estimate the transfer characteristics of the acoustic path between the output and the error signal of the adaptive controller. The results of the convergence analysis of the FXLMF algorithm indicate that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct components phase estimation error and estimated gain. In particular, the convergence is shown to be strongly affected by the accuracy of the phase response estimate. Also, we newly show that the convergence behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.285-294
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• 2016

We define new inductive mean constructed by a mean on a complete metric space, and see its convergence when the intrinsic mean is given. We also give many examples of inductive matrix means and claim that the limit of inductive mean constructed by the intrinsic mean is not the Karcher mean, in general.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.915-918
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• 2001

In this paper we study a new convergence behavior of the least mean fourth (LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach and Widrow.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.12A
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• pp.2043-2049
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• 2001

In this paper we study the convergence behavior of the least mean fourth(LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach add Widrow.

• The Journal of the Acoustical Society of Korea
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• v.18 no.2E
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• pp.3-9
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• 1999

In this paper we study the convergence behavior of the least mean fourth(LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach and Widrow/sup [1]/.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.4
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• pp.239-246
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• 2003

Application of the filtered-x Least Mean Square(LMS) adaptive filter to active noise control requires to estimate the transfer characteristics between the output and the error signal of the adaptive controller. In this paper, we derive the filtered-x adaptive noise control algorithm and analyze its convergence behavior when the acoustic noise consists of multiple sinusoids. The results of the convergence analysis of the filtered-x LMS algorithm indicate that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct components Phase estimation error and estimated gain. In particular, the convergence is shown to be strongly affected by the accuracy of the phase response estimate. Simulation results are presented to support the theoretical convergence analysis.