期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：1
页码：605-632
DOI：10.30757/ALEA.v16-22
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We introduce a two-dimensional, distribution-valued field, which wecall the quadratic field, associated with the one-dimensional Ornstein-Uhlenbeckprocess and we prove that the stationary quadratic fluctuations of the simple exclusionprocess, in the diffusive scaling, converge to this quadratic field. Moreover,we prove that this quadratic field evaluated at the diagonal corresponds to theWick-renormalized square of the Ornstein-Uhlenbeck process, and we use this newrepresentation in order to prove some small and large-time properties of it.
