Scholarlink

<p>The paper introduces a new class of random fields, supCAR&#xa0;fields, which are constructed as superpositions of continuous autoregressive random fields. These supCAR fields possess infinitely divisible marginal distributions. Their second-order properties are characterised by a novel family of covariance functions which can exhibit short- and long-range spatial dependencies. First, the existence of such fields is examined. Then, functional limit theorems for supCAR fields are derived under general assumptions. Four limiting scenarios that depend on the marginals of the underlying autoregressive fields and the specifications of the superposition are identified. Examples of specific supCAR fields, for which the assumptions and results are provided in simple, explicit forms, are presented. The obtained limit theorems can be employed for the statistical inference of supCAR&#xa0;fields.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Construction and Limit Theorems for SupCAR Fields

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月10日

查看全文
  • Illia Donhauzer,
  • Nikolai Leonenko,
  • Andriy Olenko

摘要

The paper introduces a new class of random fields, supCAR fields, which are constructed as superpositions of continuous autoregressive random fields. These supCAR fields possess infinitely divisible marginal distributions. Their second-order properties are characterised by a novel family of covariance functions which can exhibit short- and long-range spatial dependencies. First, the existence of such fields is examined. Then, functional limit theorems for supCAR fields are derived under general assumptions. Four limiting scenarios that depend on the marginals of the underlying autoregressive fields and the specifications of the superposition are identified. Examples of specific supCAR fields, for which the assumptions and results are provided in simple, explicit forms, are presented. The obtained limit theorems can be employed for the statistical inference of supCAR fields.