Local Multifractal Analysis

Barral, Julien; Durand, Arnaud; Jaffard, S.; Seuret, Stéphane

doi:10.1090/conm/601/11919

Cited by 7 publications

(5 citation statements)

References 58 publications

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“…In [1], a local spectrum for functions is defined in order to study their Hölder regularity. After the completion of our work, the paper [2] appeared. The paper deals with local multifractal analysis in Euclidean spaces for functions, measures and distributions.…”

Section: Introductionmentioning

confidence: 99%

Local multifractal analysis in metric spaces

2013

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We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild regularity conditions. On the other hand, we consider a local spectrum that can be used to gain finer information on the local behaviour of measures than its global counterpart.

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Section: Introductionmentioning

confidence: 99%

Local multifractal analysis in metric spaces

2013

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“…As was pointed out in [10, Definition 3, Lemma 4] (see also the remark below Definition 4 and Proposition 2 in [9]), the pointwise spectrum is well-defined in the sense that it does not depend on the sequence of open intervals chosen, and the local spectrum D f (A, h) on any open set A can be completely recovered from the pointwise spectrum. More precisely, for any open set A ⊂ R + and any h ≥ 0, we have…”

Section: Introduction and Main Resultsmentioning

confidence: 88%

“…It is thus relevant to consider the pointwise multifractal spectrum at a given point. Other examples with varying pointwise spectrum are studied in [19,9,6]. Definition 1.3.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Multifractality of jump diffusion processes

Yang¹

2018

Ann. Inst. H. Poincaré Probab. Statist.

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We study the local regularity and multifractal nature of the sample paths of jump diffusion processes, which are solutions to a class of stochastic differential equations with jumps. This article extends the recent work of Barral et al. who constructed a pure jump monotone Markov process with random multifractal spectrum. The class of processes studied here is much larger and exhibits novel features on the extreme values of the spectrum. This class includes Bass' stable-like processes and non-degenerate stable-driven SDEs.Nousétudions la régularité locale et la nature multifractale des trajectoires de diffusionà sauts, qui sont solutions d' une classe d'équations stochastiquesà sauts. Cet article prolonge etétend substantiellement le travail récent de Barral et al. qui ont construit un processus de Markov de sauts purs avec un spectre multifractal aléatoire. La classe considérée est beaucoup plus large et présente de nouveaux phénomènes multifractals notamment sur les valeurs extrêmes du spectre. Cette classe comprend les processus de type stable au sens de Bass et des EDS non dégénérées guidées par un processus stable. ν γ (y, du) = γ(y)u −1−γ(y) 1 [0,1] du Date: September 24, 2018.

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“…Note that (13) states that the wavelet divergence spectrum is locally invariant inside A (see [3] for a precise definition and the basic properties of the related notion of local spectrum). Remark also that if p = +∞, then this definition boils down to the condition: ∀x ∈ A, δ C (x) = −s.…”

Section: Maximally Divergent Wavelet Seriesmentioning

confidence: 99%

Divergence of wavelet series: A multifractal analysis

Esser

Jaffard

2018

Advances in Mathematics

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We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper bounds for the Hausdorff dimensions of the sets of points where a given rate of divergence occurs, and we show that these bounds are generically optimal, according to several notions of genericity.MSC2010 : Primary 42C40, 40A30 ; Secondary 28A80

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Local Multifractal Analysis

Cited by 7 publications

References 58 publications

Local multifractal analysis in metric spaces

Local multifractal analysis in metric spaces

Multifractality of jump diffusion processes

Divergence of wavelet series: A multifractal analysis

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