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 タイトル: A Limit Theorem for Weyl Transformation in Infinite-Dimensional Torus and Central Limit Theorem for Correlated Multiple Wiener Integrals 著者: Sugita, Hiroshi 発行日: 2000年 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 7 (2000), No. 1, Page 99-146 抄録: We show that under many of the probabilities on $\T^{\infty}$, infinite-dimensional torus, a random system $(1/\sqrt{N} \sum_{i=1}^N f(x_i+pα_i))$ converges to a centered Gaussian system whose covariance is determined only by the distribution of $(α_i)_{i=1}^{\infty}$ over $\T$. Moreover we show the convergence of a system of symmetric statistics to that of correlated multiple Wiener integrals defined by the Gaussian system. Also we study the central limit theorem for a sequence of the correlated multiple Wiener integrals. URI: http://hdl.handle.net/2261/1226 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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