Fractal dimensions of the Rosenblatt process

被引：4

作者：

Daw, Lara ^{[1
]}

Kerchev, George ^{[1
]}

机构：

[1] Univ Luxembourg, Dept Math, Luxembourg, Luxembourg

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2023年 / 161卷

关键词：

Rosenblatt process; Image set; Level set; Sojourn times; Hausdorff dimension; Packing dimension; Intermediate dimension; Logarithmic density; Pixel density; SAMPLE PATH PROPERTIES; PACKING DIMENSIONS; DIFFERENTIAL-EQUATIONS; ASYMPTOTIC PROPERTIES; LOCAL-TIMES; HAUSDORFF; DRIVEN; PROJECTIONS; EXPANSION; THEOREM;

D O I：

10.1016/j.spa.2023.04.001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The paper concerns the image, level and sojourn time sets associated with sample paths of the Rosenblatt process. We obtain results regarding the Hausdorff (both classical and macroscopic), packing and intermediate dimensions, and the logarithmic and pixel densities. As a preliminary step we also establish the time inversion property of the Rosenblatt process, as well as some technical points regarding the distribution of Z. (c) 2023 Published by Elsevier B.V.

引用

页码：544 / 571

页数：28

共 57 条

[1] HAUSDORFF DIMENSION AND GAUSSIAN FIELDS [J].