Long-range dependence and Appell rank

• 成果类型: Article
• 署名作者: Surgailis, D
• 署名单位: Vilnius University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 478-497
• 关键词: CENTRAL LIMIT-THEOREMS; ASYMPTOTIC-EXPANSION; gaussian fields; POLYNOMIALS; functionals

摘要

We study limit distributions of sums S-N((G)) = Sigma(t=1)(N) G(X-t) of nonlinear functions G(x) in stationary variables of the form X-t = Y-t + Z(t), where {Y-t} is a linear (moving average) sequence with long-range dependence, and {Z(t)} is a (nonlinear) weakly dependent sequence. In particular, we consider the case when {Y-t} is Gaussian and either (1) {Z(t)} is a weakly dependent multilinear form in Gaussian innovations, or (2) {Z(t)} is a finitely dependent functional in Gaussian innovations or (3) {Z(t)} is weakly dependent and independent of {Y-t}. We show in all three cases that the limit distribution of S-N((G)) is determined by the Appell rank of G(x), or the lowest k greater than or equal to 0 such that a(k) = a(k) E{G(X-0 + c)}/ac(k)\(c=0) not equal 0.