the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
In-depth analysis of a discrete p model
Abstract. Towards the end of the last century, B. Mandelbrot saw the importance, revealed the beauty, and robustly promoted (multi)fractals. Multiplicative cascades are closely related and provide simple models for the study of turbulence and chaos.
For pedagogical reasons, but also due to technical difficulties, continuous stochastic models have been favoured over discrete cascades. Particularly important are the α, the β and the p model (Lovejoy and Scherzter 2013, Chapter 3; de Wijs (1951, 1953). It is the aim of this contribution to introduce original concepts that shed new light on the latter paradigmatic cascade and allow key features to be derived in a rather elementary fashion.
To this end, we introduce and study a discrete version of the p model which is based on a new kind of sampling. Technical machinery can be kept simple, therefore formulas are explicit, proofs extend standard arguments, and potential extensions are numerous. Thus the proposed line of investigation may enrich and simplify received multifractal analyses.
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Interactive discussion
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RC1: 'Review', Anonymous Referee #1, 15 Apr 2020
- AC1: 'Author's reply to the first review', Uwe Saint-Mont, 24 Apr 2020
-
RC2: 'A review of “In-depth analysis of a discrete p model ” by U. Saint- Mont
', Anonymous Referee #2, 24 Jun 2020
- AC2: 'Author's reply to the second review', Uwe Saint-Mont, 01 Jul 2020
- EC1: 'Editor’s comment on NPG 2019-17', Daniel Schertzer, 03 Jul 2020
Interactive discussion
-
RC1: 'Review', Anonymous Referee #1, 15 Apr 2020
- AC1: 'Author's reply to the first review', Uwe Saint-Mont, 24 Apr 2020
-
RC2: 'A review of “In-depth analysis of a discrete p model ” by U. Saint- Mont
', Anonymous Referee #2, 24 Jun 2020
- AC2: 'Author's reply to the second review', Uwe Saint-Mont, 01 Jul 2020
- EC1: 'Editor’s comment on NPG 2019-17', Daniel Schertzer, 03 Jul 2020
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