| 一类多维参数高斯过程的弱逼近 |
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| 引用本文： | 李梦玉,申广君,崔静. 一类多维参数高斯过程的弱逼近[J]. 数学杂志, 2017, 37(6): 1287-1302 |
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| 作者姓名： | 李梦玉 申广君 崔静 |
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| 作者单位： | 安徽师范大学数学系, 安徽 芜湖 241000,安徽师范大学数学系, 安徽 芜湖 241000,安徽师范大学数学系, 安徽 芜湖 241000 |
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| 基金项目： | 国家自然科学基金（11271020；11401010）；安徽省杰出青年科学基金（1608085J06）；安徽省自然科学基金（1408085MA07）. |
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| 摘 要： | 本文研究了一类多维参数高斯过程的弱极限问题.在一般情况下,利用泊松过程得到了此类过程的弱极限定理,此多维参数高斯过程可表示为确定的核函数关于维纳过程的随机积分,且包含多维参数的分数布朗运动.
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| 关 键 词： | 弱收敛 高斯过程 泊松过程 分数布朗运动 |
| 收稿时间： | 2015-06-03 |
| 修稿时间： | 2016-05-16 |
WEAK APPROXIMATION FOR A CLASS OF MULTIDIMENSIONAL PARAMETER GAUSSIAN PROCESS |
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| LI Meng-yu,SHEN Guang-jun and CUI Jing. WEAK APPROXIMATION FOR A CLASS OF MULTIDIMENSIONAL PARAMETER GAUSSIAN PROCESS[J]. Journal of Mathematics, 2017, 37(6): 1287-1302 |
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| Authors: | LI Meng-yu SHEN Guang-jun CUI Jing |
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| Affiliation: | Department of Mathematics, Anhui Normal University, Wuhu 241000, China,Department of Mathematics, Anhui Normal University, Wuhu 241000, China and Department of Mathematics, Anhui Normal University, Wuhu 241000, China |
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| Abstract: | In this paper, we study the weak convergence problem of a multidimensional parameter Gaussian process. Under rather general conditions, we give an approximation in law of the process which can be represented by a stochastic integral of a deterministic kernel with respect to a standard Wiener process. The approximation processes are constructed from a standard Poisson process. An example of a Gaussian process to which this result applies is the multidimensional parameter fractional Brownian sheet with any Hurst parameter. |
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| Keywords: | weak convergence Gaussian process Poisson process fractional Brownian motion |
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