Ӧ�ø���ͳ�� 2009, 25(5) 519-530 DOI:      ISSN: 1001-4268 CN: 31-1256

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A Note on Weighted Invariance Principle
Li Linyuan:Chen Ping
Department of Mathematics and Statistics,University of New Hampshire Department of Mathematics, Southeast University
Abstract: In this note we generalize Davydov's\ucite{1}
weak invariance principle for stationary processes to a weighted
partial sums of long memory infinite moving average processes. This
note also contains some bounds on the second moments of increments
of some weighted partial sum processes of a general long memory time
series, not necessarily moving average type. These bounds are useful
in proving the tightness in uniform metric of these processes. As a
consequence of continuous mapping theorem, the probability bounds on
certain functions of random variables can be established.
Keywords: Fractional Brownian motion   infinite moving average processes   invariance principle   long range dependent data.  
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