Operator self similar stochastic processes in Rd [PDF]
Stochastic Processes and Their Applications, 1981 AbstractOperator self similar stochastic processes taking values in a finite dimensional Euclidean space are introduced and some of their properties are studied.
V K Rohatgi
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Self-similarity and Lamperti convergence for families of stochastic processes [PDF]
Lithuanian Mathematical Journal, 2011 We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of fractional Hougaard motions defined as moving averages of Hougaard Lévy process, as well as some well-known families of
Bent Jørgensen
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Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes [PDF]
Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2013 Two-particle dispersion is investigated in the context of anomalous diffusion. Two different modelling approaches related to time subordination are considered and unified in the framework of self-similar stochastic processes. By assuming a single-particle fractional Brownian motion and that the two-particle correlation function decreases ...
Gianni Pagnini, Francesco Mainardi
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A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics [PDF]
Integral Transforms and Special Functions, 2009 In this paper we present a general mathematical construction that allows us to define a parametric class of $H$-sssi stochastic processes (self-similar with stationary increments), which have marginal probability density function that evolves in time according to a partial integro-differential equation of fractional type.
Francesco Mainardi
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Noncentral Limit Theorem for the Cubic Variation of a Class of Self-Similar Stochastic Processes [PDF]
Theory of Probability and Its Applications, 2011 By using multiple Wiener–Ito stochastic integrals, we study the cubic variation of a class of self-similar stochastic processes with stationary increments (the Rosenblatt process with self-similarity order $H\in (\frac{1}{2}, 1)$). This study is motivated by statistical purposes.
Khalifa Es-Sebaiy
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Cluster Analysis on Locally Asymptotically Self-Similar Processes with Known Number of Clusters
Fractal and Fractional, 2022 We conduct cluster analysis of a class of locally asymptotically self-similar stochastic processes with finite covariance structures, which includes Brownian motion, fractional Brownian motion, and multifractional Brownian motion as paradigmatic examples.
Nan Rao, Qidi Peng, Ran Zhao
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Review article: Scaling, dynamical regimes, and stratification. How long does weather last? How big is a cloud? [PDF]
Nonlinear Processes in Geophysics, 2023 Until the 1980s, scaling notions were restricted to self-similar homogeneous special cases. I review developments over the last decades, especially in multifractals and generalized scale invariance (GSI).
S. Lovejoy
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Elliptic Self Similar Stochastic Processes [PDF]
Revista Matemática Iberoamericana, 1999 Let M be a random measure and L be an elliptic pseudo-differential operator on \mathbb{R}^d
Benassi, Albert, Roux, Daniel
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A Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks
Entropy, 2021 Dissipative accounts of structure formation show that the self-organisation of complex structures is thermodynamically favoured, whenever these structures dissipate free energy that could not be accessed otherwise.
Kai Ueltzhöffer +3 more
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Can power-law scaling and neuronal avalanches arise from stochastic dynamics? [PDF]
PLoS ONE, 2010 The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that
Jonathan Touboul, Alain Destexhe
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