Limit theorems for U-statistics with degenerate kernels and applications
具有退化内核和应用程序的 U 统计量的极限定理
基本信息
- 批准号:12640112
- 负责人:
- 金额:$ 2.18万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2000
- 资助国家:日本
- 起止时间:2000 至 2003
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The author investigated limit theorems for symmetric statistics using new technique by applying limit theorems for Banach space valued i.i.d. random variables. Usually well known Hoeffding's decomposition for symmetric scholastics cannot be used for' symmetric statistics with non-degenerate kernels. Since we consider some applications of large deviation principles for U-statistics we need to find the concrete value of the rate function. However in general it is difficult to obtain it because the rate function contains the Radon-Nikodym derivative of probability measures. Therefore we investigate another representation of the rate function defined on Eudidean space for not only mathematical but also numerical analysis of symmetric statistics.On the other hand there are some relations between symmetric statistics and approximate solutions of Ito's stochastic differential equation (SDE). The author focused on the distribution of pseudo-random numbers which are used for numerical applicati … More on of such approximate solutions and consider the error estimation of the Euler-Maruyama approximation when the distribution of underlying random variables is different from the normal distribution. Furthermore some results for stochastic differential equations with boundary conditions on mulii-dimensional domains (so-called Skorohod SDE) are obtained. We define an approximate solution of stochastic differential equation (SDE) with a reflecting barrier using the penalty method and estimate error of the approximate solution. In this note we have two aims. One is to define the approximate solution using not only a sequence of increments of Brownian motion which is independent and has normal distribution but also dependent sequence that does not obey normal distribution. Another one is, to show the advantage of the penalty method, we observe sample paths of Brownian motion with a soft boundary, i.e. any path of the Brownian motion does not reflect at the boundary immediately but is absorbed for a short period according to the strength of the path getting out of the boundary. Less
作者通过应用巴拿赫空间独立同分布的极限定理,研究了对称统计的极限定理。随机变量。通常,众所周知的对称经院学 Hoeffding 分解不能用于具有非简并核的对称统计。由于我们考虑 U 统计量大偏差原理的一些应用,我们需要找到速率函数的具体值。然而,一般来说很难获得它,因为速率函数包含概率测度的 Radon-Nikodym 导数。因此我们研究了在欧迪空间上定义的速率函数的另一种表示形式,不仅用于对称统计的数学分析,而且用于对称统计的数值分析。另一方面,对称统计与伊藤随机微分方程(SDE)的近似解之间存在一些关系。作者重点关注用于此类近似解的数值应用的伪随机数的分布,并考虑当基础随机变量的分布与正态分布不同时,Euler-Maruyama 近似的误差估计。此外,还获得了多维域上具有边界条件的随机微分方程(所谓的 Skorohod SDE)的一些结果。我们使用罚分法定义了带有反射障碍的随机微分方程(SDE)的近似解,并估计了近似解的误差。在这篇文章中,我们有两个目标。一是不仅使用独立且具有正态分布的布朗运动增量序列,而且使用不服从正态分布的相关序列来定义近似解。另一种是,为了显示惩罚方法的优点,我们观察具有软边界的布朗运动的样本路径,即布朗运动的任何路径不会立即在边界处反射,而是根据离开边界的路径的强度在短时间内被吸收。较少的
项目成果
期刊论文数量(26)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
S.Kanagawa, Y.Saisho: "Strong Approximation of Reflecting Brownian Motion Using Penalty Method and its Application to Computer Simulation"Monte Carlo Methods Application. 6巻. 105-114 (2000)
S.Kanakawa,Y.Saisho:“使用惩罚方法反映布朗运动的强近似及其在计算机模拟中的应用”蒙特卡罗方法应用卷。 6. 105-114 (2000)
- DOI:
- 发表时间:
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- 影响因子:0
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- 通讯作者:
金川秀也, 小川重義: "確率微分方程式の数値解法"日本数学会「数学」論説. 53・2. 125-138 (2001)
神奈川秀哉、小川重吉:“随机微分方程的数值解”日本数学会社论 53・2(2001 年)。
- DOI:
- 发表时间:
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- 影响因子:0
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S.Kanagawa: "Some Remarks on Strong Approximation of Reflecting Brownian Motion Using Penalty Method"Proceedings of Neural, Parallel & Scientific Computations. Vol.2. 63-70 (2002)
S.Kanakawa:“关于使用惩罚方法反映布朗运动的强近似的一些评论”神经并行学论文集
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- 影响因子:0
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S.Kanagawa, S.Ogawa: "Numerical solution of the stochastic differential equation, applications2"Sugaku Expositions. (to appear). (2005)
S.神奈川,S.Okawa:“随机微分方程的数值解,应用2”Sugaku Expositions。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
S.Kanagawa, Y.Saisho: "Strong approximation of reflecting Brownian Motion using 1peralty method and its approkivration ts computer simulation"Monte Carlo Methods Appl.. 6. 105-114 (2000)
S.Kanakawa、Y.Saisho:“使用 1peralty 方法反映布朗运动的强近似及其计算机模拟”Monte CarloMethods Appl.. 6. 105-114 (2000)
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KANAGAWA Shuya其他文献
KANAGAWA Shuya的其他文献
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{{ truncateString('KANAGAWA Shuya', 18)}}的其他基金
Change-point analysis for time series using asymptotic theory for symmetric statistics
使用对称统计渐近理论对时间序列进行变点分析
- 批准号:
20540140 - 财政年份:2008
- 资助金额:
$ 2.18万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Limit theorems for U- and V-statistics for dependent random variables and their applications
因随机变量的 U 和 V 统计量的极限定理及其应用
- 批准号:
16540124 - 财政年份:2004
- 资助金额:
$ 2.18万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
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