Related papers: Random Wavelet Series: Theory and Applications
Many new models of wave turbulence -- frozen, mesoscopic, laminated, decaying, sand-pile, etc. -- have been developed in the last decade aiming to solve problems seemingly not solvable in the framework of the existing wave turbulence theory…
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
The wavelet transform and related techniques are used to analyze singular and fractal signals. The normalized wavelet scalogram is introduced to detect singularities including jumps, cusps and other sharply changing points. The wavelet…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
A disordered structure embedding an active gain material and able to lase is called random laser (RL). The RL spectrum may appear either like a set of sharp resonances or like a smooth line superimposed to the fluorescence. A recent letter…
We consider series of the form $\sum a_n \{n\cdot x\}$, where $n\in\Z^{d}$ and $\{x\}$ is the sawtooth function. They are the natural multivariate extension of Davenport series. Their global (Sobolev) and pointwise regularity are studied…
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…
Classification of time series signals has become an important construct and has many practical applications. With existing classifiers we may be able to accurately classify signals, however that accuracy may decline if using a reduced…
Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…
This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon…
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
Wavelet-type random series representations of the well-known Fractional Brownian Motion (FBM) and many other related stochastic processes and fields have started to be introduced since more than two decades. Such representations provide…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
Time series data analysis is a critical component in various domains such as finance, healthcare, and meteorology. Despite the progress in deep learning for time series analysis, there remains a challenge in addressing the non-stationary…
We use singular value decomposition techniques to generalize the wavelet transform modulus maxima method to the multifractal analysis of vector-valued random fields. The method is calibrated on synthetic multifractal 2D vector measures and…
The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed…
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…