Fractal dimensions of the Rosenblatt process

Lara Daw and George Kerchev

Stochastic Processes and their Applications, 2023, vol. 161, issue C, 544-571

Abstract: 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.

Keywords: Rosenblatt process; Image set; Level set; Sojourn times; Hausdorff dimension; Packing dimension; Intermediate dimension; Logarithmic density; Pixel density (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:161:y:2023:i:c:p:544-571

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DOI: 10.1016/j.spa.2023.04.001

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