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

摘要

Weshowthatundermanyoftheprobabilitieson$T^{infty}$,infinite-dimensionaltorus,arandomsystem$(1/sqrt{N}sum_{i=1}^Nf(x_i+p?±_i))$convergestoacenteredGaussiansystemwhosecovarianceisdeterminedonlybythedistributionof$(?±_i)_{i=1}^{infty}$over$T$.MoreoverweshowtheconvergenceofasystemofsymmetricstatisticstothatofcorrelatedmultipleWienerintegralsdefinedbytheGaussiansystem.AlsowestudythecentrallimittheoremforasequenceofthecorrelatedmultipleWienerintegrals.