Fractal dimensions of the Rosenblatt process
Lara Daw, George Kerchev
TL;DR
This paper investigates the fractal properties of the Rosenblatt process, including dimensions and densities of its sample paths, and establishes key properties like time inversion and distribution characteristics.
Contribution
It provides new results on the Hausdorff, packing, and intermediate dimensions of the Rosenblatt process's path sets, and proves the time inversion property.
Findings
Determined Hausdorff and packing dimensions of the Rosenblatt process paths
Established the time inversion property of the Rosenblatt process
Analyzed the distribution and density properties of the process
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 .
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Taxonomy
TopicsAdvanced Queuing Theory Analysis · Scheduling and Optimization Algorithms · Stochastic processes and financial applications