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Machine learning unlocks robust convergence for chemical process simulations
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Complete Convergence of Martingale Arrays
Journal of Theoretical Probability, 1998A sequence \(\{U_n, n\geq 1\}\) of random variables is said to converge completely to the constant \(c\) if \(\sum^\infty_{n= 1} P(| U_n- c|> \varepsilon)< \infty\) for all \(\varepsilon> 0\). The definition was introduced by \textit{P. L. Hsu} and \textit{H. Robbins} [Proc. Natl. Acad. Sci.
Ghosal, Subhashis, Chandra, Tapas K.
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Complete convergence and complete moment convergence for martingale difference sequence
Acta Mathematica Sinica, English Series, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Xue Jun, Hu, Shu He
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Completion of Semiuniform Convergence Spaces
Applied Categorical Structures, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Complete convergence and complete moment convergence for widely orthant-dependent random variables
Communications in Statistics - Theory and Methods, 2016In this paper, we first establish the complete convergence for weighted sums of widely orthant-dependent (WOD, in short) random variables by using the Rosenthal type maximal inequality.
Yang Ding +4 more
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2008
Abstract We have already noted some seventeenth- and eighteenth-century discussions of convergence (or the lack of them) in 8.3, and in this Chapter we take up the nineteenth-century continuation of the same story. One of the most powerful tools available to early nineteenth-century mathematicians investigating convergence turned out to ...
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Abstract We have already noted some seventeenth- and eighteenth-century discussions of convergence (or the lack of them) in 8.3, and in this Chapter we take up the nineteenth-century continuation of the same story. One of the most powerful tools available to early nineteenth-century mathematicians investigating convergence turned out to ...
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Completely Convex Functions and Convergence
SIAM Journal on Mathematical Analysis, 1979A function $f(x)$ is completely convex (c.c.) on $[0,1]$ if $( - 1)^k f^{(2k)} (x) \geqq 0$ for $k \geqq 0$ and all x in $[0,1]$. This paper studies the convergence of the partial sums of the Maclaurin series of the function; in particular, how quickly the partial sums turn into a c.c. function. It is shown that no matter where the series is truncated,
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Complete convergence for arrays
Periodica Mathematica Hungarica, 1992Let \(\{(X_{nk}\), \(1\leq k\leq n)\), \(n\geq 1\}\) be an array of rowwise independent random variables. We extend and generalize some recent results due to \textit{T.-C. Hu}, \textit{F. Móricz} and \textit{R. L. Taylor} [Acta Math. Hung. 54, No. 1/2, 153-162 (1989; Zbl 0685.60032)] concerning complete convergence, in the sense of \textit{P. L.
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Complete convergence for α-mixing sequences
Statistics & Probability Letters, 1993Let \(X_ n\) be a sequence of \(\alpha\)-mixing random variables with mean zero, uniformly bounded \(r\)-th moments and the mixing coefficient \(\alpha(n)\) and let \(S_ n\) denote the partial sum of the first \(n\) \(X\) variables. It is proved that for any \(\varepsilon>0\), \[ \sum^ \infty_{n=1}n^{p\alpha-2}P\left(\max_{i\leq n}| S_ i|\geq ...
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