2024-03-29T01:10:42Z
https://repository.dl.itc.u-tokyo.ac.jp/oai
oai:repository.dl.itc.u-tokyo.ac.jp:00040241
2022-12-19T04:15:26Z
312:6865:7017:7025
9:504:6868:7019:7026
A Limit Theorem for Weyl Transformation in Infinite-Dimensional Torus and Central Limit Theorem for Correlated Multiple Wiener Integrals
Sugita, Hiroshi
138838
415
application/pdf
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.
departmental bulletin paper
Graduate School of Mathematical Sciences, The University of Tokyo
2000
application/pdf
Journal of mathematical sciences, the University of Tokyo
1
7
99
146
AA11021653
13405705
https://repository.dl.itc.u-tokyo.ac.jp/record/40241/files/jms070106.pdf
eng