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投影下的Gronwall不等式 总被引:7,自引:1,他引:6
本文对J.K.Hale曾提出的一类广泛的投影下的Gronwal不等式问题作了讨论,对满足u(t)≤a(t)+∫0tb(t-s)u(s)ds+∫0∞c(s)u(t+s)ds,(?)t≥0的函数u(t)∈Cb0(R+,R+)作了估计.其结果对讨论微分方程的有界解、不变流形及其Foliation和进一步讨论奇性Gronwal不等式都有意义 相似文献
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本文构造出一个以{θk=k/(n+1)π}nk=1为插值节点的f(θ)∈C2π且为奇函数的修正的三角插值多项式Wn(f;r,θ)(r为自然数).Wn(f;r,θ)对每个以2π为周期的奇连续函数都能在全实轴上一致地收敛到f(θ);若f(θ)∈Cj2π(0≤j≤r-1)且是奇的,Wn(f;r,θ)对其收敛阶均达到最 相似文献
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本文考虑了线性模型中回归系数β=(β1,…,βp)′和误差方差σ2的联立经验Bayes(EB)估计.在二次损失下,利用密度函数及其编导数的核估计构造出参数θ=(β1,…,βp,σ2)的联立EB估计,在一定条件下证明了θ的联立EB估计的收敛速度任意接近于1.最后、给出了一个实例. 相似文献
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设Bm(f,·)为函数f在d维单纯形σ上的n阶Bernstein多项式,本文对f∈Cr(σ)及f∈Cr+2(σ)给出了f的各阶编导数用Bn(f,·)相应偏导数逼近的误差估计.同时也考虑了整系数Bernstein多项式的Lp模估计 相似文献
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本文主要探讨下列周期系数微分方程dy/dt=(A1(t)y+A2(t)y2+A3(t)y3)/(a0(t)+a1(t)y+a2(t)y2)(**)的周期解个数问题,利用方程(**)解的差率法得到了方程(**)周期解的个数定理.本文仅在Ai(t),aj(t)(i=1,2,3,j=0,1,2)是连续周期函数的条件下得到这一结论,从而减弱了文[2]中相应定理的条件,即Ai(t),aj(t)均是连续可微的周期函数. 相似文献
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设S2(T)为三角域T的二阶剖分,本文给出在S2(T)下分片二次函数f(P)∈C1(T)的Bernstcin多项式的退化性及递推公式。这里的条件S2(T)及C1(T)类都是重要的。我们举例说明更一般情况下分片二次函数Bernstcin多项式的复杂性。 相似文献
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Let (X
i) be a sequence of m × m i.i.d. stochastic matrices with distribution . Then
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is the distribution of X
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X
n–1
...X
1. Simple sufficient conditions for the weak convergence of (
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) are presented here. An extremely simple (and verifiable) necessary and sufficient condition is provided for m= 3. The method for m= 3 works for m> 3 even though calculations are more involved for higher values of m. We also discuss the purity of the limit distribution for m2. 相似文献
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利用随机的Bernstein多项式研究随机逼近问题具有一定的意义.借助弱收敛的概念,从分布函数的角度,讨论了随机Bernstein多项式依分布收敛问题.同时,与依概率收敛结果相比较,以此说明Bernstein多项式序列依分布收敛适用的范围更广. 相似文献
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Petr Lachout 《Acta Appl Math》2003,78(1-3):243-250
The paper introduces an extension of the epi-convergence, the lower semicontinuous approximation and the epi-upper semicontinuous approximation of random real functions in distribution. The new notions could be helpful tools for sensitivity analyzes of stochastic optimization problems. The research is evoked by S. Vogel and continues the research started by Vogel and the author. 相似文献
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In this paper, the proof of a Trotter-Kato type theorem in a variable Banach space is given and some special cases and examples are considered. 相似文献
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Remco van der Hofstad Gerard Hooghiemstra Piet Van Mieghem 《Random Structures and Algorithms》2002,20(4):519-539
In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519–539, 2002 相似文献
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《数学季刊》2016,(2):162-170
Let {Xnk, k≥1, n≥1} be an array of rowwise negatively superadditive depen-dent random variables and {an, n ≥ 1} be a sequence of positive real numbers such that an ↑ ∞. Under some suitable conditions, Lr convergence of a1n 1max≤j≤n ied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables. fl fl fl fl jP k=1 Xnk fl fl flfl is stud-ied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables. 相似文献
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Let be an ideal. We say that a sequence of real numbers is -convergent to if for every neighborhood U of y the set of n's satisfying ynU is in . Basing upon this notion we define pointwise -convergence and -convergence in measure of sequences of measurable functions defined on a measure space with finite measure. We discuss the relationship between these two convergences. In particular we show that for a wide class of ideals including Erdős–Ulam ideals and summable ideals the pointwise -convergence implies the -convergence in measure. We also present examples of very regular ideals such that this implication does not hold. 相似文献
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Jacod, Jakubowski和M\'emin讨论了与单个独立增量过程$X$的误差过程$^n\!X =X_t-X_{[nt]/n}$相关的积分误差过程$Y^n(X)$和$Z^{n,p}(X)$, 研究了半鞅序列$\{(nY^n(X),nZ^{n,p}(X))\}_{n\ge 1}$的极限定理. 记半鞅序列$\{(nY^n(X),nZ^{n,p}(X))\}_{n\ge1}$的极限过程为$(Y(X),Z^p(X))$, Jacod等给出了其极限过程$(Y(X)$, $Z^p(X))$的表达式. 本文将研究半鞅序列$\{X^n\}_{n\ge1}$积分误差的极限过程$Y(X^n)$和$Z^{p}(X^n)$的收敛定理, 主要研究半鞅序列$\{(X^n,Y(X^n),Z^p(X^n))\}_{n\ge1}$的依分布弱收敛和依分布稳定收敛. 相似文献