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Related papers: Levy Stability Index from Multifractal Spectrum

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As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…

Analysis of PDEs · Mathematics 2018-12-12 Lucie Baudouin , Alexandre Seuret , Frédéric Gouaisbaut

This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some…

Optimization and Control · Mathematics 2025-06-16 L. A. Mozelli , R. L. S. Adriano

In this paper we present an estimator for the three-dimensional parameter $(\sigma, \alpha, H)$ of the linear fractional stable motion, where $H$ represents the self-similarity parameter, and $(\sigma, \alpha)$ are the scaling and stability…

Statistics Theory · Mathematics 2020-03-26 Mathias Mørck Ljungdahl , Mark Podolskij

We study the stability of a vector field associated to a nearly-integrable Hamiltonian dynamical system to which a dissipation is added. Such a system is governed by two parameters, named the perturbing and dissipative parameters, and it…

Dynamical Systems · Mathematics 2012-02-14 Alessandra Celletti , Christoph Lhotka

In this paper we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural…

Methodology · Statistics 2018-02-20 Stepan Mazur , Dmitry Otryakhin , Mark Podolskij

Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations…

We establish inequalities for assessing the distance between the distribution of errors of partially observed high-frequency statistics of multidimensional L\'evy processes and that of a mixed Gaussian random variable. Furthermore, we…

Probability · Mathematics 2025-04-14 Chiara Amorino , Arturo Jaramillo , Mark Podolskij

Stochastic resonance phenomenon induced by non-Gaussian L\'evy noise in a second-order bistable system is investigated. The signal-noise-ratio for different parameters is computed by an efficient numerical scheme. The influences of the…

Statistical Mechanics · Physics 2013-09-06 Yong Xu , Juanjuan Li , Jing Feng , Huiqing Zhang , Wei Xu , Jinqiao Duan

Multiple scattering of light by resonant vapor is characterized by Levy-type superdiffusion with a step size distribution $P(x) \propto 1/x^{1+{\alpha}}$, with $0 < {\alpha} < 2$. The Levy parameter ${\alpha}$ was measured from $P(x)$,…

This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…

Dynamical Systems · Mathematics 2017-08-18 Bin Zhou

In this article, we determine the multivariate multifractal Legendre spectra of shifted L{\'e}vy functions. This allows us to explore how the validity of the multivariate multifractal formalism depends on the shift parameter. This article…

Dynamical Systems · Mathematics 2025-05-15 Stéphane Jaffard , Lingmin Liao , Qian Zhang

We propose a new method for the estimation of a semiparametric tempered stable L\'{e}vy model. The estimation procedure combines iteratively an approximate semiparametric method of moment estimator, Truncated Realized Quadratic Variations…

Econometrics · Economics 2022-02-25 José E. Figueroa-López , Ruoting Gong , Yuchen Han

Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…

Fluid Dynamics · Physics 2021-06-30 L. Moriconi

To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, a stochastic collision model is investigated. We consider the dynamics of a tracer particle of mass $M$, undergoing elastic collisions with…

Statistical Mechanics · Physics 2009-11-10 Eli Barkai

For $n$ equidistant observations of a L\'evy process at time distance $\Delta_n$ we consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal-Getoor index in a non- or semiparametric manner.…

Statistics Theory · Mathematics 2013-04-05 Markus Reiß

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…

Data Analysis, Statistics and Probability · Physics 2009-11-07 Jan W. Kantelhardt , Stephan A. Zschiegner , Eva Koscielny-Bunde , Armin Bunde , Shlomo Havlin , H. Eugene Stanley

The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large…

Fluid Dynamics · Physics 2024-06-28 Joel Daou , Prabakaran Rajamanickam

We consider longwave mode of the interface instability in the system comprising of two immiscible fluid layers. The fluids fill out plane horizontal cavity which is subjected to horizontal harmonic vibration. The analysis is performed…

patt-sol · Physics 2007-05-23 Mikhail V. Khenner , Dmitrii V. Lyubimov

Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies. A computational analysis is conducted to…

Dynamical Systems · Mathematics 2012-01-31 Huiqin Chen , Jinqiao Duan , Chengjian Zhang

In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…

Analysis of PDEs · Mathematics 2021-04-09 Mohammad Akil , Ali Wehbe