CENTRAL LIMIT THEOREMS FOR STATIONARY RANDOM FIELDS UNDER WEAK DEPENDENCE WITH APPLICATION TO AMBIT AND MIXED MOVING AVERAGE FIELDS

• 成果类型: Article
• 署名作者: Curato, Imma Valentina; Stelzer, Robert; Stroeh, Bennet
• 署名单位: Ulm University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1722
• 发表日期: 2022
• 页码: 1814-1861
• 关键词: stochastic integration; driven; supou

摘要

We obtain central limit theorems for stationary random fields employing a novel measure of dependence called theta-lex weak dependence. We show that this dependence notion is more general than strong mixing, that is, it applies to a broader class of models. Moreover, we discuss hereditary properties for theta-lex and eta-weak dependence and illustrate the possible applications of the weak dependence notions to the study of the asymptotic properties of stationary random fields. Our general results apply to mixed moving average fields (MMAF) and ambit fields. We show general conditions such that MMAF and ambit fields, with the volatility field being an MMAF or a p-dependent random field, are weakly dependent. For all the models mentioned above, we give a complete characterization of their weak dependence coefficients and sufficient conditions to obtain the asymptotic normality of their sample moments. Finally, we give explicit computations of the weak dependence coefficients of MSTOU processes and analyze under which conditions the developed asymptotic theory applies to CARMA fields.