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Convergence conditions of the least squares method
Journal of Mathematical Sciences, 1994Least squares estimation of parameters is considered. Sufficient conditions of strong consistency are obtained for a regression model in the presence of random errors.
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Necessary Conditions for the Convergence of Fourier Series
Analysis Mathematica, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Condition for Convergence in Mean of Trigonometric Series
Mathematical Notes, 2001Consider an arbitrary trigonometric series \[ \sum^\infty_{n=-\infty} c_n e^{inx}\tag{1} \] and set \[ S_n(x):= \sum^n_{k=-n} c_k e^{ikx},\quad \sigma_n(x):= {1\over n+1} \sum^n_{k=0} S_k(x),\quad n\geq 0. \] If (1) is a Fourier series, then its partial sums \(S_n\) converge (respectively, are bounded) in the metric of \(L\) if and only if ...
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Types of conditional convergence
2005Summary: The aim of this paper is to investigate relations between different types of conditional convergence. Results presented in this paper generalize theorems obtained by \textit{P. Fernandez} [Bol. Soc. Bras. Mat. 3, 13--16 (1972; Zbl 0344.60008)] and \textit{A. R. Padmanabhan} [Math. Jap. 15, 111--117 (1970; Zbl 0234.60038)].
Nowak, Wioletta, Zięba, Wiesław
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Some conditions for subsequential convergence and ordinary convergence
2019In this paper, we obtain certain conditions in terms of the regularly generated sequences under which (u(n)) converges subsequentially or converges.
Canak, Ibrahim, Totur, Umit
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Conditions for Convergence to Degenerate Processes
Theory of Probability & Its Applications, 1974openaire +2 more sources
On the Rate of Convergence in the “Conditional” Invariance Principle
Theory of Probability & Its Applications, 1978openaire +3 more sources