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Chaos: An Interdisciplinary Journal of Nonlinear Science
We introduce novel perspectives on stochastic self-similarity and stationarity, addressing limitations and extensions of classical definitions when applied to heterogeneous and multifractal processes. We propose a new notion of stochastic self-similarity encompassing processes with random parameters and establish a corresponding Lamperti transformation.
Hubert Woszczek +3 more
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We introduce novel perspectives on stochastic self-similarity and stationarity, addressing limitations and extensions of classical definitions when applied to heterogeneous and multifractal processes. We propose a new notion of stochastic self-similarity encompassing processes with random parameters and establish a corresponding Lamperti transformation.
Hubert Woszczek +3 more
openaire +3 more sources
Physical Review E, 2007
Efficient tools to characterize stochastic processes are discussed. Quantifiers originally proposed within the framework of information theory, like entropy and statistical complexity, are translated into wavelet language, which renders the above quantifiers into tools that exhibit the important "localization" advantages provided by wavelet theory. Two
L, Zunino +5 more
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Efficient tools to characterize stochastic processes are discussed. Quantifiers originally proposed within the framework of information theory, like entropy and statistical complexity, are translated into wavelet language, which renders the above quantifiers into tools that exhibit the important "localization" advantages provided by wavelet theory. Two
L, Zunino +5 more
openaire +2 more sources
BASIC PROPERTIES AND CHARACTERIZATION OF STOCHASTICALLY SELF-SIMILAR PROCESSES IN Rd
Fractals, 1999The classical notion of self-similarity (ss) for random X(t) as invariance under the group of positive affine transformations {X→ arX, t→rt; ar>0} is extended by allowing ar to be a random variable. The resulting property of "stochastic self-similarity" (sss) is applied to both ordinary and generalized random processes in Rd, d≥1.
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Time-scale analyses and self-similar stochastic processes
1994A number of different physical situations (e.g.,“1 /f noise,” turbulence, texture analysis,… ) give rise to fractal or fractal-like signals, modeled as samples of self-similar processes. This motivates the development of specific methods for characterizing self-similarity structures in signals and for efficiently estimating the corresponding scaling ...
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Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136), 2002
We propose a doubly stochastic point process for modeling traffic data. The traffic intensity is modeled as a self-similar process and is generated by applying an inverse orthogonal wavelet transform to a sequence of independent random sequences, having different variances at different scales.
BARBAROSSA, Sergio +3 more
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We propose a doubly stochastic point process for modeling traffic data. The traffic intensity is modeled as a self-similar process and is generated by applying an inverse orthogonal wavelet transform to a sequence of independent random sequences, having different variances at different scales.
BARBAROSSA, Sergio +3 more
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Self-similar Chaotic Processes in Dynamical Systems of Nonlinear Stochastic Maps
2021George Vostrov +2 more
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Quantum Stochastic Processes and Quantum non-Markovian Phenomena
PRX Quantum, 2021Kavan Modi, Simon Milz
exaly
Self-exciting jump processes and their asymptotic behaviour
Stochastics, 2022Kristina Rognlien Dahl +1 more
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Stochastic Processes in Cell Biology
Interdisciplinary Applied Mathematics, 2021Paul Bressloff
exaly
Stochastic Resonance, Self-Organization and Information Dynamics in Multistable Systems
Entropy, 2016Gregoire Nicolis
exaly