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Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data
We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method...
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Log-Infinitely Divisible Multifractal Processes
We define a large class of multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These...
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Modelling fluctuations of financial time series: from cascade process to stochastic volatility model
In this paper, we provide a simple, “generic” interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of...
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Singularity spectrum of multifractal functions involving oscillating singularities
We give general mathematical results concerning oscillating singularities and we study examples of functions composed only of oscillating...
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Nucleotide composition effects on the long-range correlations in human genes
We use the wavelet transform to investigate the fractal scaling properties of coding and noncoding human DNA sequences. We find that the strength of...
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Oscillating singularities on cantor sets: A grand-canonical multifractal formalism
The singular behavior of functions is generally characterized by their Hölder exponent. However, we show that this exponent poorly characterizes...
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Scale Invariance and Beyond: What Can We Learn from Wavelet Analysis ?
In many situations in physics as well as in some applied sciences, one is faced to the problem of characterizing very irregular functions [1–8]. The...
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Wavelet Analysis
The central problem of three-dimensional fully developed turbulence is the energy cascading process. It has resisted all attempts at a full...
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Singularity spectrum of fractal signals from wavelet analysis: Exact results
The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov...
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Wavelet Analysis of Fractal Signals Application to Fully Developed Turbulence Data
The recently developed multifractal formalism1 has proven particularly fruitful in the characterization of singular measures arising in a variety of...
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Fibonacci Sequences in Diffusion-Limited Aggregation
Pattern formation in systems far from equilibrium is a subject of considerable current interest1–6. Recently, much effort has been directed towards...