西尔皮斯基垫圈上的分数稳定随机场

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY Stochastic Processes and their Applications Pub Date : 2024-09-03 DOI:10.1016/j.spa.2024.104481

Fabrice Baudoin , Céline Lacaux

引用次数: 0

摘要

我们定义并研究了西尔潘斯基垫圈上的分数稳定随机场。这种场的形式定义为 (-Δ)-sWK,α，其中 Δ 是垫圈上的拉普拉斯算子，WK,α 是稳定随机量。对 Δ 的 Neumann 和 Dirichlet 边界条件都进行了考虑。我们获得了样本路径正则性和缩放特性。我们开发的技术是通用的，并可扩展到巴洛分式空间的更一般设置。

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Fractional stable random fields on the Sierpiński gasket

We define and study fractional stable random fields on the Sierpiński gasket. Such fields are formally defined as

{(- Δ)}^{- s} W_{K, α}

, where

Δ

is the Laplace operator on the gasket and

W_{K, α}

is a stable random measure. Both Neumann and Dirichlet boundary conditions for

Δ

are considered. Sample paths regularity and scaling properties are obtained. The techniques we develop are general and extend to the more general setting of the Barlow fractional spaces.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.