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Square-mean almost periodic solutions nonautonomous stochastic differential equations
Paul H. Bezandry,Toka Diagana
Electronic Journal of Differential Equations , 2007,
Abstract: This paper concerns the square-mean almost periodic solutions to a class of nonautonomous stochastic differential equations on a separable real Hilbert space. Using the so-called "Acquistapace-Terreni" conditions, we establish the existence and uniqueness of a square-mean almost periodic mild solution to those nonautonomous stochastic differential equations.
Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients
Omar Mellah,Paul Raynaud de Fitte
Electronic Journal of Differential Equations , 2013,
Abstract: We show that, contrarily to what is claimed in some papers, the nontrivial solutions of some stochastic differential equations with almost periodic coefficients are never mean square almost periodic (but they can be almost periodic in distribution).
一类非自治随机微分方程的均方渐近概周期解
SQUARE-MEAN ASYMPTOTICALLY ALMOST PERIODIC SOLUTION ON A CLASS OF NONAUTONOMOUS STOCHASTIC DIFFERENTIAL EQUATIONS

作者,姚慧丽,王健伟
- , 2016,
Abstract: 本文研究了一类在可分Hilbert空间中的非自治随机微分方程的均方渐近概周期解.利用"Acquistapace-Terreni"条件,开方族和Banach不动点原理讨论了该类随机微分方程的均方渐近概周期解的存在唯一性,推广了该类随机微分方程的均方概周期解的存在唯一性问题.
In this papre, the square-mean asymptotically almost periodic solution is studied on a class of nonautonomous stochastic differential equations in a separable Hilbert space. By using the "Acquistapace-Terreni" conditions, evolution families and Banach fixed point theorem, the existence and uniqueness of square-mean asymptotically almost periodic solution on this kind of nonautonomous stochastic differential equations are discussed. The problems on the existence and uniqueness of square-mean almost periodic solutions on this kind of equation are generalized
Square-mean almost automorphic mild solutions to some stochastic differential equations in a Hilbert space
Chang Yong-Kui,Zhao Zhi-Han,N'Guérékata Gaston
Advances in Difference Equations , 2011,
Abstract: This article deals primarily with the existence and uniqueness of square-mean almost automorphic mild solutions for a class of stochastic differential equations in a real separable Hilbert space. We study also some properties of square-mean almost automorphic functions including a compostion theorem. To establish our main results, we use the Banach contraction mapping principle and the techniques of fractional powers of an operator. Mathematics Subject Classification (2000) 34K14, 60H10, 35B15, 34F05.
伪概自首随机过程分解及应用
COMPOSITION OF PSEUDO AUTOMORPHIC STOCHASTIC PROCESS AND APPLICATIONS

作者,周辉,周宗福,乔宗敏
- , 2017,
Abstract: 在较弱Lipschitz条件下,本文建立伪概自守随机过程分解定理,该定理推广了已知结果.利用所建立理论的性质,本文获得了一类随机微分方程的伪概自守弱解的存在唯一性条件.
In this paper, a composition theorem for pseudo-almost automorphic stochastic process is established under a weaker Lipschitz condition. The composition theorem is more general than some known results. Using these properties, we obtain the existence and uniqueness of pseudoalmost automorphic mild solutions for a class of stochastic differential equations
一类随机微分方程均方s渐进ω周期解的存在性
EXISTENCE OF SQUARE-MEAN s-ASYMPTOTICALLY ω-PERIODIC SOLUTIONS TO SOME STOCHASTIC DIFFERENTIAL EQUATIONS

作者,刘敬怀,宋晓秋,张理涛
- , 2018,
Abstract: 本文研究了在可分的实Hilbert空间中一类随机微分方程均方s渐进ω周期温和解的存在性问题.利用均方s渐进ω周期随机过程理论及Banach不动点定理,获得了此类方程均方s渐进ω周期温和解的存在及唯一性结果.最后给出相关例子来验证理论结果.
This paper is concerned with the existence of square-mean s-asymptotically ω-periodic mild solutions to some stochastic differential equations in a real separable Hilbert space. By using the new theorem of square-mean s-asymptotically ω-periodicity for stochastic process and Banach fixed point theorem, we obtain the existence and uniqueness of square-mean s-asymptotically ω-periodic mild solutions to the equations. To illustrate the abstract result, a concrete example is given
On the Restricted Almost Unbiased Ridge Estimator in Logistic Regression  [PDF]
Nagarajah Varathan, Pushpakanthie Wijekoon
Open Journal of Statistics (OJS) , 2016, DOI: 10.4236/ojs.2016.66087
Abstract: In this article, the restricted almost unbiased ridge logistic estimator (RAURLE) is proposed to estimate the parameter in a logistic regression model with exact linear re-strictions when there exists multicollinearity among explanatory variables. The performance of the proposed estimator over the maximum likelihood estimator (MLE), ridge logistic estimator (RLE), almost unbiased ridge logistic estimator (AURLE), and restricted maximum likelihood estimator (RMLE) with respect to different ridge parameters is investigated through a simulation study in terms of scalar mean square error.
Almost periodic solutions of difference systems
Shunian Zhang
Chinese Science Bulletin , 1998, DOI: 10.1007/BF03183502
Abstract: For linear difference systems, a rather general result on the existence of almost periodic solutions is established, which also gives the explicit expression of the almost periodic solution in terms of the coefficient matrix and the nonhomogeneous term. The obtained result confirms not only the existence, but also the uniqueness as well as the uniform asymptotic stability of the almost periodic solution. As an application, a criterion on the existence of almost periodic solutions of the second order difference equations is derived.
Stochastic Approximation Method for Fixed Point Problems  [PDF]
Ya. I. Alber, C. E. Chidume, Jinlu Li
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.312A293
Abstract: We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.

Reducibility for a Class of Two-Dimensional almost Periodic System with Small Perturbation  [PDF]
Fanhui Meng, Wenhua Qiu
Advances in Pure Mathematics (APM) , 2021, DOI: 10.4236/apm.2021.1112061
Abstract: This paper focuses on the reducibility of two-dimensional almost periodic system with small perturbation. We use the KAM iterative method to get the reducibility by an almost periodic transformation. The system has been reduced to a simple form. So we have dealt with the small perturbation problem of the almost periodic system.
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