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Related papers: Linear Multifractional Stable Motion: representati…

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Linear Fractional Stable Motion (LFSM) of Hurst parameter $H$ and of stability parameter $\al$, is one of the most classical extensions of the well-known Gaussian Fractional Brownian Motion (FBM), to the setting of heavy-tailed stable…

Statistics Theory · Mathematics 2013-04-11 Antoine Ayache , Julien Hamonier

The main goal of this paper is to construct a wavelet-type random series representation for a random field $X$, defined by a multistable stochastic integral, which generates a multifractional multistable Riemann-Liouville (mmRL) process…

Probability · Mathematics 2020-04-14 Antoine Ayache , Julien Hamonier

Since the middle of the 90's, multifractional processes have been introduced for overcoming some limitations of the classical Fractional Brownian Motion model. In their context, the Hurst parameter becomes a Holder continuous function H(?)…

Statistics Theory · Mathematics 2015-05-29 Antoine Ayache , Julien Hamonier

Linear Multifractional Stable Motion (LMSM), denoted by $\{Y(t):t\in\R\}$, has been introduced by Stoev and Taqqu in 2004-2005, by substituting to the constant Hurst parameter of a classical Linear Fractional Stable Motion (LFSM), a…

Probability · Mathematics 2013-02-08 Antoine Ayache , Julien Hamonier

Estimating accurate high-dimensional transformations remains very challenging, especially in a clinical setting. In this paper, we introduce a multiscale parameterization of deformations to enhance registration and atlas estimation in the…

Optimization and Control · Mathematics 2025-01-31 Fleur Gaudfernau , Eléonore Blondiaux , Stéphanie Allassonnière , Erwan Le Pennec

Multifractional processes extend the concept of fractional Brownian motion by replacing the constant Hurst parameter with a time-varying Hurst function. This extension allows for modulation of the roughness of sample paths over time. The…

Probability · Mathematics 2025-03-11 Antoine Ayache , Andriy Olenko , Nemini Samarakoon

In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in Ayache, Roueff and Xiao (2007). By using this representation, in the case where the sample…

Statistics Theory · Mathematics 2008-12-18 Antoine Ayache , François Roueff , Yimin Xiao

The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar…

Other Computer Science · Computer Science 2014-10-06 Mikhail Prisheltsev

Non-Gaussian Harmonizable Fractional Stable Motion (HFSM) is a natural and important extension of the well-known Fractional Brownian Motion to the framework of heavy-tailed stable distributions. It was introduced several decades ago;…

Probability · Mathematics 2023-10-10 Antoine Ayache , Yimin Xiao

Time-modulated arrays (TMAs) can effectively perform beamsteering over the first positive harmonic pattern by applying progressively delayed versions of stair-step approximations of a sine waveform to the antenna excitations. In this…

Signal Processing · Electrical Eng. & Systems 2024-02-01 R. Maneiro-Catoira , J. Brégains , José A. García-Naya , L. Castedo

This paper presents a new approach for tackling the shift-invariance problem in the discrete Haar domain, without trading off any of its desirable properties, such as compression, separability, orthogonality, and symmetry. The paper…

Computer Vision and Pattern Recognition · Computer Science 2017-05-23 Mais Alnasser , Hassan Foroosh

This paper focuses on real-time all-frequency image-based rendering using an innovative solution for run-time computation of light transport. The approach is based on new results derived for non-linear phase shifting in the Haar wavelet…

Computer Vision and Pattern Recognition · Computer Science 2017-05-23 Mais Alnasser , Hassan Foroosh

It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet…

Methodology · Statistics 2013-09-11 Guy P. Nason , Kara N. Stevens

Linear fractional stable motion, denoted by $\{X_{H,\al}(t)\}_{t\in \R}$, is one of the most classical stable processes; it depends on two parameters $H\in (0,1)$ and $\al\in (0,2)$. The parameter $H$ characterizes the self-similarity…

Statistics Theory · Mathematics 2013-02-08 Antoine Ayache , Julien Hamonier

This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…

Statistics Theory · Mathematics 2025-03-19 Henry Antonio Palasciano , Marina I. Knight , Guy P. Nason

Let $Z^H= \{Z^H(t), t \in \R^N\}$ be a real-valued $N$-parameter harmonizable fractional stable sheet with index $H = (H_1, \ldots, H_N) \in (0, 1)^N$. We establish a random wavelet series expansion for $Z^H$ which is almost surely…

Probability · Mathematics 2019-03-12 Antoine Ayache , Narn-Rueih Shieh , Yimin Xiao

We construct a wavelet-based almost sure uniform approximation of fractional Brownian motion (fBm) B_t^(H), t in [0, 1], of Hurst index H in (0, 1). Our results show that by Haar wavelets which merely have one vanishing moment, an almost…

Probability · Mathematics 2013-07-04 Dawei Hong , Shushuang Man , Jean-Camille Birget , Desmond Lun

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…

Probability · Mathematics 2023-03-10 Antoine Ayache , Julien Hamonier , Laurent Loosveldt

The common methods of spectral analysis for multivariate ($n$-dimensional) time series, like discrete Frourier transform (FT) or Wavelet transform, are based on Fourier series to decompose discrete data into a set of trigonometric model…

Methodology · Statistics 2022-10-26 Martin Seilmayer , Ferran Garcia Gonzalez , Thomas Wondrak

A first type of Multifractional Process with Random Exponent (MPRE) was constructed several years ago in (Ayache, Taqqu, 2005) by replacing in a wavelet series representation of Fractional Brownian Motion (FBM) the Hurst parameter by a…

Probability · Mathematics 2018-03-08 Antoine Ayache , Céline Esser , Julien Hamonier
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