论文标题
静态随机字段的中央限制定理在弱依赖性下，应用于范围和混合移动平均场
Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields
论文作者
论文摘要
我们获得了使用一种新型依赖度量的固定随机字段的中心限制定理，称为$θ$ -LEX弱依赖性。我们表明，这种依赖性概念比强烈的混合更一般，即它适用于更广泛的模型。此外，我们讨论了$θ$ -LEX和$η$ weak依赖性的遗传性质，并说明了弱依赖性概念对固定随机场的渐近性特性的可能应用。我们的总体结果适用于混合运动平均场（简称MMAF）和范围场。我们显示的一般条件是，MMAF和ABBIT场是MMAF或$ p $依赖的随机场，这是微弱的依赖性。对于上述所有模型，我们对它们弱依赖系数和足够条件的完整表征，以获得其样品矩的渐近正态性。最后，我们对MSTOU过程的弱依赖系数进行明确的计算，并在哪个条件下对开发的渐近理论进行分析适用于Carma田地。
We obtain central limit theorems for stationary random fields employing a novel measure of dependence called $θ$-lex weak dependence. We show that this dependence notion is more general than strong mixing, i.e., it applies to a broader class of models. Moreover, we discuss hereditary properties for $θ$-lex and $η$-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 in short) 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.
