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ALMOST SURE CONVERGENCE ON CHAOSES
Proceedings of the American Mathematical Society, 2019 International audienceWe present several new phenomena about almost sure convergence on homogeneous chaoses that include Gaussian Wiener chaos and homogeneous sums in independent random variables.
Poly, Guillaume, Zheng, Guangqu
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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 and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation [PDF]
Abstract and Applied Analysis, 2014 The convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in Lp-sense.
Qian Guo, Xueyin Tao
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Convergence in probability and almost sure with applications
Stochastic Processes and their Applications, 2001 A necessary and sufficient condition is given for the convergence in probability of a stochastic process {Xt}. Moreover, as a byproduct, an almost sure convergent stochastic process {Yt} with the same limit as {Xt} is identified. In a number of cases {Yt}
Cohn, Harry, Harry Cohn
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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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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)
Zuoxiang Peng, Saralees Nadarajah
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On the Almost Sure Rate of Convergence of Linear Stochastic Approximation Algorithms
IEEE Transactions on Information Theory, 2004 The almost sure rate of convergence of linear stochastic approximation algorithms is analyzed in this correspondence. As the main result, it is demonstrated that their almost sure rate of convergence is equivalent to the almost sure rate of convergence ...
Tadić, VB
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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.
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Lpand almost sure convergence of a Milstein scheme for stochastic partial differential equations
Stochastic Processes and Their Applications, 2013 In this paper, Lp convergence and almost sure convergence of the Milstein approximation of a partial differential equation of advection-diffusion type driven by a multiplicative continuous martingale is proven.
Andrea Barth, Annika Lang
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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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