Wiener过程在Hlder范数下的泛函重对数定律(英文)

本文借助于Hlder范数在函数空间中诱导出的强拓扑下的大偏差公式,得到了Wiener过程在Hlder范数下的泛函重对数定律.     

Wiener过程在Hoelder范数下的泛函重对数定律

本文借助于Hoelder范数在函数空间中诱导出的强拓扑下的大偏差公式，得到了Wiener过程在Hoelder范数下的泛函重对数定律．     

$l^p$-值Wiener过程在H\"older范数下的泛函重对数定律[英文]

在H\"older范数生成的强拓扑下, 基于$l^2$-值Wiener过程的大偏差公式, 本文得到了H\"older范数意义下, $l^2$-值Wiener过程的泛函重对数定律, 也得到了$l^p$-值Wiener过程的泛函重对数定律, 在这里$1\leq p<\infty$.     

大偏差与lp-值Wiener过程在H(o)lder范数下的泛函连续模

本文在Holder范数生成的强拓扑下,建立了l~2-值Wiener过程的大偏差公式,从而得到了l~2-值与l~p-值Wiener过程在Holder范数下的泛函连续模.     

lp-值Wiener过程子列C-R型增量在H?lder范数下的泛函样本轨道性质

得到了l~p-值Wiener过程(1≤p∞)子列C-R型增量,在H?lder范数下的泛函样本轨道性质,推广了l~p-值Wiener过程的泛函重对数定律.     

大偏差与l~p-值Wiener过程在Hlder范数下的泛函连续模

本文在Holder范数生成的强拓扑下,建立了l~2-值Wiener过程的大偏差公式,从而得到了l~2-值与l~p-值Wiener过程在Holder范数下的泛函连续模.     

Brown运动增量在H?lder范数下的局部泛函Chung重对数律

本文利用Brown运动在H?lder范数下的大偏差和小偏差,得到了Brown运动增量在H?lder范数下的局部泛函Chung重对数律.     

Brown运动连续模在H(o)lder范数下的拟必然收敛速度

本文中,用Brown运动在H(o)lder范数下关于Cr,p-容度的大偏差与小偏差,得到了Brown运动连续模在H(o)lder范数下关于Cr,p-容度的泛函收敛速度.     

扩散过程在Hlder范数下的局部Strassen重对数律

在该文中,作者应用扩散过程在Holder范数下的大偏差得到了扩散过程在Holder范数下的局部Strassen重对数律．并且还得到了重It■积分的泛函重对数律．     

κ-维Brown运动的泛函重对数定律

本文研究了 κ-维Brown运动的泛函样本轨道性质．利用了一致范数在高维连续函数空间生成的拓扑下建立大偏差公式的方法，获得了 κ-维Brown运动的泛函重对数定律．     

Banach函数空间的H(o)lder不等式

本文给出了基本不等式‖nⅡi=1ai,ai≤‖n∑i=1,aiai(ai>0,ai>0,n∑i=1,ai=1)的一个确界形式,以此统一得出Banach函数空间Lp(E,u),L∞(E,u),L∞(R),C(R)等的 H(O)lder函数不等式.     

Laws of the Iterated Logarithm for the Local U-Statistic Process

Laws of the iterated logarithm are established for the local U-statistic process. This entails the development of probability inequalities and moment bounds for U-processes that should be of separate interest. The local U-statistic process is based upon an estimator of the density of a function of several i.i.d. variables proposed by Frees (J. Am. Stat. Assoc. 89, 517–525, 1994). As a consequence, our results are directly applicable to the derivation of exact rates of uniform in bandwidth consistency in the sup and in the L _p norms for these estimators. Research of E. Giné partially supported by NSA Grant H98230-04-1-0075. Research of D.M. Mason partially supported by NSA Grant MDA904-02-1-0034 and NSF Grant DMS-0503908.     

两参数OU过程的钟重对数律（英）

在本文中，我们证明了两参数OU过程的钟重对数律。     

On the coverage of strassen-type sets by sequences of Wiener processes

LetW ₁,W ₂,... be a sequence of Wiener processes and let K _T 1 be a function ofT1. We consider the limiting behavior asT of the random set of functions defined by . Under suitable assumptions imposed uponK _T , we show that covers asymptotically (in the sense of the Hausdorff set-metric induced by the sup-norm distance) Strassen-type sets equal, up to a multiplicative constant, to the limit set of functions obtained in the classical functional law of the iterated logarithm. Extensions of these results to arrays and increments of Wiener processes in the range studied by Book and Shore(²) are also provided.     

Laws of the iterated logarithm for iterated Wiener processes

The recent interest in iterated Wiener processes was motivated by apparently quite unrelated studies in probability theory and mathematical statistics. Laws of the iterated logarithm (LIL) were independently obtained by Burdzy⁽²⁾ and Révész⁽¹⁷⁾. In this work, we present a functional version of LIL for a standard iterated Wiener process, in the spirit of functional asymptotic results of an ²-valued Gaussian process given by Deheuvels and Mason⁽⁹⁾ in view of Bahadur-Kiefer-type theorems. Chung's liminf sup LIL is established as well, thus providing further insight into the asymptotic behavior of iterated Wiener processes.