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Multifractal Analysis of Complex Random Cascades

Abstract : We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new phenomena in multifractal analysis of continuous functions. In particular, we find examples of statistically self-similar such functions obeying the multifractal formalism and for which the support of the singularity spectrum is the whole interval [0, ∞].
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https://hal.inria.fr/hal-00790872
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Submitted on : Thursday, February 21, 2013 - 1:36:55 PM
Last modification on : Thursday, April 29, 2021 - 11:53:46 PM

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Julien Barral, Xiong Jin. Multifractal Analysis of Complex Random Cascades. Communications in Mathematical Physics, Springer Verlag, 2010, 297 (1), pp.129-168. ⟨10.1007/s00220-010-1030-y⟩. ⟨hal-00790872⟩

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