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国家自然科学基金(10571159)

作品数:18 被引量:13H指数:2
相关作者:林正炎张荣茂程宗毛陈守全张彩伢更多>>
相关机构:浙江大学西南大学北京大学更多>>
发文基金:国家自然科学基金国家教育部博士点基金中国博士后科学基金更多>>
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18 条 记 录,以下是 1-10
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Functional Limit Theorems for d-dimensional FBM in H lder Norm被引量:2
2006年
In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.
Zheng Yan LINWen Sheng WANGKyo Shin HWANG
随机变量序列函数的几乎处处中心极限定理被引量:6
2008年
该文证明了随机元序列的一个一般的几乎处处中心极限定理,并把这一结论应用于随机变量序列的函数.
陈守全林正炎
关键词:几乎处处中心极限定理随机函数U统计量
广义Lévy单的样本轨道性质被引量:1
2006年
设X(t)是下指数为α取值于R^d的N参数广义Lévy单,■={(s,t]=∏(s_i,t_i],s_i<t_i},E(x,Q)={t∈Q:X(t)=x},Q∈■,是X在点x处的水平集,X(Q)={x:■t∈Q,使得X(t)=x}为X在Q上的像集.本文探讨了X(t)局部时存在性及其增量的大小.同时,也得到了水平集E(x,Q)Hausdorff维数和X(Q)一致维数上界的结果.
张荣茂林正炎
关键词:局部时HAUSDORFF维数
一类N参数Gauss过程的异常震动点集合的Hausdorff维数
2007年
引进了一类N参数Gauss过程,它具有比N参数Wiener过程更为一般的性质.给出了此类N参数Gauss过程的异常震动点集的定义,并且定义了此异常震动点集的Hausdorff维数.研究了此类过程的异常震动点集Hausdorff维数,给出了它的一个确切的表达式,从而获得了与Zacharie(2001)的有关两参数Wiener过程的类似的结果.考虑的参数点集是一般的超长方体.而不是Zacharie(2001)考虑的超正方体.在此更为一般的情况下,首先建立了文中引进的过程的Fernique不等式.利用此不等式和Slepian引理,证明了过程的Lévy连续模定理.Zacharie(2001)关于Hausdorff维数公式的证明依赖于两参数Wiener过程的独立增量性,而这里引进的过程不具有这种性质,因此,必须采用新的证明途径.
林正炎程宗毛
关键词:连续模HAUSDORFF维数
Hausdorff dimension of set generated by exceptional oscillations of a class of N-parameter Ganssian processes
2007年
A class of N-parameter Gaussian processes are introduced, which are more general than the N-parameter Wiener process. The definition of the set generated by exceptional oscillations of a class of these processes is given, and then the Hausdorff dimension of this set is defined. The Hausdorff dimensions of these processes are studied and an exact representative for them is given, which is similar to that for the two-parameter Wiener process by Zacharie (2001). Moreover, the time set considered is a hyperrectangle which is more general than a hyper-scluare used by Zacharie (2001). For this more general case, a Fernique-type inequality is established and then using this inequality and the Slepian lemma, a Levy's continuity modulus theorem is shown. Independence of increments is required for showing the representative of the Hausdorff dimension by Zacharie (2001). This property is absent for the processes introduced here, so we have to find a different way.
林正炎程宗毛
Maximal speed of particles in super-Lévy process
2008年
We introduce a super-Lévy process and study maximal speed of all particles in the range and the support of the super-Lévy process. The state of historical super-Lévy process is a measure on the set of paths. We study the maximal speed of all particles during a given time period, which turns out to be a function of the packing dimension of the time period. We calculate the Hausdorff dimension of the set of a-fast paths in the support and the range of the historical super-Lévy process.
林正炎程宗毛
超Lévy过程的粒子的最大速度
2008年
引进了超Lévy过程,研究了在它的域(range)和支撑中粒子的最大速度问题.历史的超Lévy过程的状态是一个轨道集的测度.研究了在给定的时间集E里全部粒子的最大速度,结果表明它是E的packing维数的函数.最后还计算了在历史的超Lévy过程的域和支撑中的a-快轨道集的Hausdorff维数.
林正炎程宗毛
关键词:连续模HAUSDORFF维数LÉVY过程BROWN运动
Moduli of Continuity of a Class of N-parameter Gaussian Processes and Their Fast Points
2008年
We study the moduli of continuity of a class of N-parameter Gaussian processes and get some results on'the packing dimension of the set of their fast points.
Zheng Yan LINZong Mao CHENG
Precise Rates in the Law of the Iterated Logarithm under Dependence Assumptions被引量:1
2008年
Let {X, X1, X2,...} be a strictly stationaryφ-mixing sequence which satisfies EX = 0,EX^2(log2{X})^2〈∞and φ(n)=O(1/log n)^Tfor some T〉2.Let Sn=∑k=1^nXk and an=O(√n/(log2n)^γ for some γ〉1/2.We prove that limε→√2√ε^2-2∑n=3^∞1/nP(|Sn|≥ε√ESn^2log2n+an)=√2.The results of Gut and Spataru (2000) are special cases of ours.
Wel Dong LIU Zheng Yan LIN
Results on Local Times of a Class of Multiparameter Gaussian Processes
2006年
In this paper, we introduce a class of Gaussian processes Y={Y(t):t∈R^N},the so called hifractional Brownian motion with the indcxes H=(H1,…,HN)and α. We consider the (N, d, H, α) Gaussian random field x(t) = (x1 (t),..., xd(t)),where X1 (t),…, Xd(t) are independent copies of Y(t), At first we show the existence and join continuity of the local times of X = {X(t), t ∈ R+^N}, then we consider the HSlder conditions for the local times.
Zong-mao ChengXiu-yun WangZheng-yan Lin
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