一类多维参数高斯过程的弱逼近  

WEAK APPROXIMATION FOR A CLASS OF MULTIDIMENSIONAL PARAMETER GAUSSIAN PROCESS

作　　者：李梦玉[1] 申广君[1] 崔静[1] 

机构地区：[1]安徽师范大学数学系,安徽芜湖241000

出　　处：《数学杂志》2017年第6期1287-1302,共16页Journal of Mathematics

基　　金：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)

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.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.

关 键 词：弱收敛 高斯过程 泊松过程 分数布朗运动 

分 类 号：O211.4[理学—概率论与数理统计]