A Limit Theorem for Weyl Transformation in Infinite-Dimensional Torus and Central Limit Theorem for Correlated Multiple Wiener Integrals
Vol. 7 (2000), No. 1, Page 99--146.
Sugita, Hiroshi ; Takanobu, Satoshi
A Limit Theorem for Weyl Transformation in Infinite-Dimensional Torus and Central Limit Theorem for Correlated Multiple Wiener Integrals
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Abstract:
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.
Mathematics Subject Classification (1991): Primary 60F05
Mathematical Reviews Number: MR1749982
Received: 1999-04-20
