A Limit Theorem for Weyl Transformation in Infinite-Dimensional Torus and Central Limit Theorem for Correlated Multiple Wiener Integrals

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概要

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• 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.

• 東京大学の論文

著者

• Sugita Hiroshi

  Graduate School Mathematics Kyushu University

• Takanobu Satoshi

  Department of Mathematics, Faculty of Science, Kanazawa University

• Takanobu Satoshi

  Department Of Mathematics Faculty Of Science Kanazawa University

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