Results 11 to 20 of about 9,441 (247)
Almost Sure Convergence for the Maximum and the Sum of Nonstationary Guassian Sequences
Journal of Inequalities and Applications, 2010 Let (Xn, n≥1) be a standardized nonstationary Gaussian sequence. Let Mn= max{Xk,1≤k≤n} denote the partial maximum and Sn=∑k−1nXk for the partial sum with σn= (Var Sn)1/2.
Shengli Zhao, Zuoxiang Peng, Songlin Wu
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Estimating Smoothness and Optimal Bandwidth for Probability Density Functions
Stats, 2022 The properties of non-parametric kernel estimators for probability density function from two special classes are investigated. Each class is parametrized with distribution smoothness parameter. One of the classes was introduced by Rosenblatt, another one
Dimitris N. Politis +2 more
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Some remarks on the ergodic theorem for $U$-statistics
Comptes Rendus. Mathématique, 2023 In this note, we investigate the convergence of a $U$-statistic of order two having stationary ergodic data. We will find sufficient conditions for the almost sure and $L^1$ convergence and present some counter-examples showing that the $U$-statistic ...
Dehling, Herold +2 more
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Almost sure convergence on chaoses
Proceedings of the American Mathematical Society, 2019 We present several new phenomena about almost sure convergence on homogeneous chaoses that include Gaussian Wiener chaos and homogeneous sums in independent random variables. Concretely, we establish the fact that almost sure convergence on a fixed finite sum of chaoses forces the almost sure convergence of each chaotic component.
Poly, Guillaume, Zheng, Guangqu
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Some Types of Convergence for Negatively Dependent Random Variables under Sublinear Expectations
Discrete Dynamics in Nature and Society, 2019 In this paper, we research complete convergence and almost sure convergence under the sublinear expectations. As applications, we extend some complete and almost sure convergence theorems for weighted sums of negatively dependent random variables from ...
Ruixue Wang, Qunying Wu
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DAVENPORT SERIES AND ALMOST-SURE CONVERGENCE [PDF]
The Quarterly Journal of Mathematics, 2010 We consider Davenport-like series with coecients in l 2 and discuss L 2 -convergence as well as almost-everywhere convergence. We give an example where both fail to hold. We next improve former sucient conditions under which these convergences are true.
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Convergence rates of theta-method for NSDDEs under non-globally Lipschitz continuous coefficients [PDF]
Bulletin of Mathematical Sciences, 2019 This paper is concerned with strong convergence and almost sure convergence for neutral stochastic differential delay equations under non-globally Lipschitz continuous coefficients.
Li Tan, Chenggui Yuan
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Almost sure convergence of weighted sums [PDF]
Miskolc Mathematical Notes, 2013 Summary: Let \(\{X:X_n,\;n\geq 1\}\) be a sequence of identically distributed random variables and \(\{a_{i,n}:\;1\leq i\leq n\}\) be a triangular array of constants. In this short paper, we establish a general almost sure convergence theorem for the weighted sum \(S_n=\sum^n_{i=1} a_{i,n} X_i\). Our results improve those of \textit{S. H.
Miao, Yu, Xu, Shoufang
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Probabilistic norms and statistical convergence of random variables [PDF]
Surveys in Mathematics and its Applications, 2009 The paper extends certain stochastic convergence of sequences of Rk -valued random variables (namely, the convergence in probability, in Lp and almost surely) to the context of E-valued random variables.
Mohamad Rafi Segi Rahmat +1 more
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On the almost sure convergence of sums [PDF]
Statistics & Probability Letters, 2021 Two counterexamples, addressing questions raised in \cite{AD} and \cite{PZ}, are provided. Both counterexamples are related to chaoses. Let $F_n=Y_n+Z_n$. It may be that $F_n\overset{a.s.}\longrightarrow 0$, $F_n\overset{L_{2+ }}\longrightarrow 0$ and $E\bigl\{\sup_n\,\abs{F_n}^ \bigr\}0$ and $Y_n$ and $Z_n$ belong to chaoses of uniformly bounded ...
Pratelli Luca, Rigo Pietro
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