کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1145945 | 1489686 | 2013 | 17 صفحه PDF | دانلود رایگان |
A general moment bound for sums of products of Gaussian vector’s functions extending the moment bound in Taqqu (1977, Lemma 4.5) [28] is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved. This theorem extends the previous results of Breuer and Major (1983) [5], Arcones (1994) [1] and others. A Berry–Esseen-type bound in the above-mentioned central limit theorem is derived following Nourdin et al. (2011) [20]. Two applications of the above results are discussed. The first one refers to the asymptotic behavior of a roughness statistic for continuous-time Gaussian processes and the second one is a central limit theorem satisfied by long memory locally stationary processes.
Journal: Journal of Multivariate Analysis - Volume 114, February 2013, Pages 457–473