Lévy Matters II
Recent Progress in Theory and Applications: Fractional Lévy Fields, and Scale Functions
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Article
Open AccessTransition of the Simple Random Walk on the Ice Model Graph
The 6-vertex model holds significance in various mathematical and physical domains. The configurations of the 6-vertex model correspond to the paths in multigraphs. This article focuses on calculating the tran...
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Article
Determinants of Antithrombotic Treatment for Atrial Fibrillation in Octogenarians: Results of the OCTOFA Study
Atrial fibrillation, the most frequent form of arrhythmia, affects 5–15% individuals aged > 80 years. Stroke is a major risk for atrial fibrillation patients. The benefits of anticoagulant therapy clearly outw...
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Book
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Book
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Chapter
Introduction
Fractals everywhere! This is the title of a bestseller, but it is also a reality: Fractals are really everywhere. What a change since the days of Charles Hermite declaring “I turn away with fright and horror o...
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Chapter
Fractional Lévy Fields
In this survey, we would like to summarize most of the results concerning the so-called fractional Lévy fields in a way as self-contained as possible. Beside the construction of these fields, we are interested...
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Chapter
Preliminaries
In this chapter we have collected some results that will be used in the sequel of the book. We have divided these results in two parts. In the first one we recall some facts concerning stochastic processes. In...
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Chapter
Asymptotic Self-Similarity
Self-similarity, as described in the previous chapter, is a global property, and as such, may be to rigid for some applications. Actually, in many situations the self-similarity parameter H is expected to change ...
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Chapter
Simulations
The aim of this chapter is to give simulations of some of fractional fields introduced in the previous chapters. Our main concern here is algorithmic and heuristic : We would like to provide tools to probabili...
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Chapter
Self-Similarity
Self-similarity is a major part of the mathematics. One can refer to [53] for a general reference. The self-similarity literature is quite confusing for beginners since the statement of very elementary facts m...
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Chapter
Statistics
In this chapter we would like to discuss the use of the models introduced in the previous chapters for Statistics. One of the major question is the estimation of the various parameters in those models. The com...
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Article
Adaptive sequential design for regression on multi-resolution bases
This work investigates the problem of construction of designs for estimation and discrimination between competing linear models. In our framework, the unknown signal is observed with the addition of a noise an...
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Article
On Tightness and Weak Convergence in the Approximation of the Occupation Measure of Fractional Brownian Motion
In this paper we consider approximations of the occupation measure of the Fractional Brownian motion by means of some functionals defined on regularizations of the paths. In a previous article Berzin and León ...
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Chapter
Regularity and Identification of Generalized Multifractional Gaussian Processes
In this article a class of multifractional processes is introduced, called Generalized Multifractional Gaussian Process (GMGP). For such multifractional models, the Hurst exponent of the celebrated Fractional ...
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Article
Small and Large Scale Behavior of the Poissonized Telecom Process
The stable Telecom process has infinite variance and appears as a limit of renormalized renewal reward processes. We study its Poissonized version where the infinite variance stable measure is replaced by a Po...
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Chapter
Self-Similarity and Intermittency
In this paper, we propose a class of stochastic processes having an extended self-similarity property as well as intermittency. These notions are characterized with two parameters, and we propose statistical e...
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Article
Identification of the Hurst Index of a Step Fractional Brownian Motion
We propose a semi-parametric estimator for a piece-wise constant Hurst coefficient of a step fractional Brownian motion (SFBM). For the applications, we want to detect abrupt changes of the Hurst index (which ...
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Chapter and Conference Paper
From Self-Similarity to Local Self-Similarity: the Estimation Problem
In this article we review some methods used to identify the order H of a fractional Brownian motion. This discussion is introduced to see how such techniques can be extended to locally self-similar processes. Mor...
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Book and Conference Proceedings
