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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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Almost sure convergence of extreme order statistics
Electronic Journal of Statistics, 2009 Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Saralees Nadarajah
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Polynomial asymptotic stability of damped stochastic differential equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2004 The paper studies the polynomial convergence of solutions of a scalar nonlinear It\^{o} stochastic differential equation\[dX(t) = -f(X(t))\,dt + \sigma(t)\,dB(t)\] where it is known, {\it a priori}, that $\lim_{t\rightarrow\infty} X(t)=0$, a.s.
John Appleby, D. Mackey
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Almost Sure Convergence of Generalized $U$-Statistics
Annals of Probability, 1977 Almost sure convergence of generalized $U$-statistics and von Mises' differentiable statistical functions is studied with the help of the general $L \log L$ martingale convergence theorem.
exaly +4 more sources
Almost sure exponential stability of numerical solutions for stochastic delay differential equations [PDF]
, 2010 Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (
Szpruch, Lukasz, Wu, Fuke, Mao, Xuerong
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Estimating Cumulative Distribution Function Using Gamma Kernel [PDF]
Journal of Sciences, Islamic Republic of Iran, 2022 In this article, we propose the gamma kernel estimator for the cumulative distribution functions with nonnegative support. We derive the asymptotic bias and variance of the proposed estimator in both boundary and interior regions and show that it is free
Behzad Mansouri +3 more
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Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations [PDF]
, 2011 By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Euler–Maruyama (EM) approximations of stochastic functional differential equations (SFDEs) can share the almost sure ...
Wu, Fuke +2 more
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Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations [PDF]
, 2011 This is a continuation of the first author's earlier paper [1] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler-Maruyama (EM) method can reproduce the almost sure exponential stability of the ...
Shen, Yi, Mao, Xuerong, Gray, Alison
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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 $F_n\overset{a.s.}\longrightarrow 0$, $F_n\overset{L_{2+δ}}\longrightarrow 0$ and $E\bigl\{\sup_n\,\abs{F_n}^δ\bigr\}0$ and $Y_n$ and $Z_n$ belong to chaoses of uniformly bounded ...
Pratelli Luca, Rigo Pietro
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Results in Control and Optimization, 2023 In this paper, split step theta balanced Euler approximations for stochastic time-varying delay Hopfield neural networks (HNN) with distributed delays are examined for their exponential stability and strong convergence.
Pichamuthu Mayavel +1 more
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