2016/01/14 by Jean–François Muzy, J. F. Muzy, Rachel Baïle +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Computer science #Dimension (graph theory) #Distribution (mathematics) #Financial Risk and Volatility Modeling #Fractal #Fractal dimension #Geometry #Mandelbrot set #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Physics #Pure mathematics #Scaling #Statistical physics #physics.ao-ph #physics.data-an
paper · pdf · doi:10.1103/physreve.93.052305
published as Phys. Rev. E 93, 052305 (2016) · 12 Figures
arxiv created 2016/01/14 · openalex publication_date 2016/05/06 · arxiv updated 2016/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a variant of continuous random cascade models that extends former constructions introduced by Barral-Mandelbrot and Bacry-Muzy in the sense that they can be supported by sets of arbitrary fractal dimension. The so-introduced sets are exactly self-similar stationary versions of random Cantor sets formerly introduced by Mandelbrot as "random cutouts." We discuss the main mathematical properties of our construction and compute its scaling properties. We then illustrate our purpose on several numerical examples and we consider a possible application to rainfall data. We notably show that our model allows us to reproduce remarkably the distribution of dry period durations.