相关论文: Random Wavelet Series: Theory and Applications

We study the regularity properties of random wavelet series constructed by multiplying the coefficients of a deterministic wavelet series with unbounded I.I.D. random variables. In particular, we show that, at the opposite to what happens…

We study the global and local regularity properties of random wavelet series whose coefficients exhibit correlations given by a tree-indexed Markov chain. We determine the law of the spectrum of singularities of these series, thereby…

We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "waveforms" with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and…

The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…

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…

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…

In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise…

Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…

In this paper, we determine the almost sure multifractal spectrum of a class of random functions constructed as sums of pulses with random dilations and translations. In addition, the continuity modulii of these functions is investigated.

We investigate stochastic processes possessing scale invariance properties which we refer to as multifractal processes. The examples of such processes known so far do not go much beyond the original cascade construction of Mandelbrot. We…

A general method to construct wavelet function on real number ffeld is proposed in this article,which is based on finite length sequence.This finite length sequence is called the seed sequence, and the corresponding wavelet function is…

We discuss properties of random fractals by means of a set of numbers that characterize their universal properties. This set is the generalized singularity specturm that consists of the usual spectrum of mulitfractal dimensions and the…

Positive $T$-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We…

Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…

Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and…

We consider multifractal random wavelet series built from Gibbs measures, and study the singularity spectra associated with the graph and range of these functions restricted to their iso-H\"older sets. To obtain these singularity spectra,…

We introduce a class of multifractal processes, referred to as Multifractal Random Walks (MRWs). To our knowledge, it is the first multifractal processes with continuous dilation invariance properties and stationary increments. MRWs are…

In this article, we construct two families of nonsymmetrical multifractal fields. One of these families is used for the modelization of the velocity field of turbulent flows.

The theory of random sets is demonstrated to prove useful for the theory of random operators. A random operator is here defined by requiring the graph to be a random set. It is proved that the spectrum and the set of eigenvalues of random…

We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…