广义线性多重分形稳定片：局部时间的存在性和联合连续性

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2021-06-24 DOI:10.3150/22-bej1479

Yujia Ding, Qidi Peng, Yimin Xiao

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引用次数: 0

摘要

我们引入了广义线性多重分形稳定片（LMSS）的概念，其中α∈（0，2]）包括线性多重分形布朗片（α=2）和线性多重分形稳定性片（α<2）。本文的目的是研究LMSS局部时间的存在性和联合连续性，以及局部时间在集合变量中的局部Hölder条件。在本文的主要结果中，定理2.4为LMSS的局部时间的存在提供了一个充分必要的条件；定理3.1给出了局部时间联合连续性的一个充分条件；定理4.1证明了集合变量中局部时间的一个尖锐的局部Hölder条件。所有这些定理都显著地改进了文献中关于多分数布朗表和线性多分数稳定表的局部时间的现有结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Linear multifractional stable sheets in the broad sense: Existence and joint continuity of local times

We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) with α ∈ (0 , 2] , to include both linear multifractional Brownian sheets ( α = 2 ) and linear multifractional stable sheets ( α < 2 ). The purpose of the present paper is to study the existence and joint continuity of the local times of LMSS, and also the local Hölder condition of the local times in the set variable. Among the main results of this paper, Theorem 2.4 provides a sufﬁcient and necessary condition for the existence of local times of LMSS; Theorem 3.1 shows a sufﬁcient condition for the joint continuity of local times; and Theorem 4.1 proves a sharp local Hölder condition for the local times in the set variable. All these theorems improve signiﬁcantly the existing results for the local times of multifractional Brownian sheets and linear multifractional stable sheets in the literature.

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.