Browsing by Author "Sposini, V."
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Centreofmass like superposition of OrnsteinUhlenbeck processes: A pathway to nonautonomous stochastic differential equations and to fractional diffusion
D’Ovidio, M.; Vitali, S.; Sposini, V.; Sliusarenko, O.; Paradisi, P.; Castellani, G.; Pagnini, G. (20181025)We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centreofmass ... 
Exact distributions of the maximum and range of random diffusivity processes
Grebenkov, D. S.; Sposini, V.; Metzler, R.; Oshanin, G.; Seno, F. (20210209)We study the extremal properties of a stochastic process $x_t$ defined by the Langevin equation ${\dot {x}}_{t}=\sqrt{2{D}_{t}}\enspace {\xi }_{t}$, in which $\xi_t$ is a Gaussian white noise with zero mean and $D_t$ is a ... 
Exact firstpassage time distributions for three random diffusivity models
Grebenkov, D. S.; Sposini, V.; Metzler, R.; Oshanin, G.; Seno, F. (20210104)We study the extremal properties of a stochastic process $x_t$ defined by a Langevin equation $\dot{x}= \sqrt{2D_o V (B_t )} \xi_t$, where $\xi$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, ... 
Finiteenergy Lévytype motion through heterogeneous ensemble of Brownian particles
Sliusarenko, O.; Vitali, S.; Sposini, V.; Paradisi, P.; Chechkin, A.V.; Castellani, G.; Pagnini, G. (20190201)Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling $x \sim t^\delta$ with $\delta \neq 1/2$ in the probability density function (PDF). Anomalous diffusion can emerge jointly ... 
Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
Sposini, V.; Vitali, S.; Paradisi, P.; Pagnini, G. (20210724)In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a powerlaw heterogeneity. Within the framework of the continuous time random walk, the ... 
Langevin equation in complex media and anomalous diffusion
Vitali, S.; Sposini, V.; Sliusarenko, O.; Paradisi, P.; Castellani, G.; Pagnini, G. (20180730)The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such ... 
The random diffusivity approach for diffusion in heterogeneous systems
Sposini, V. (20201216)The two hallmark features of Brownian motion are the linear growth $\langle x^2(t) \rangle = 2 D d t$ of the mean squared displacement (MSD) with diffusion coefficient $D$ in $d$ spatial dimensions, and the Gaussian ... 
Random diffusivity from stochastic equations: comparison of two models for Brownian yet nonGaussian diffusion
Sposini, V.; Chechkin, A.V.; Seno, F.; Pagnini, G.; Metzler, R. (201804)A considerable number of systems have recently been reported in which Brownian yet nonGaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the ... 
Singletrajectory spectral analysis of scaled Brownian motion
Sposini, V.; Metzler, R.; Oshanin, G. (201906)A standard approach to study timedependent stochastic processes is the power spectral density (PSD), an ensembleaveraged property defined as the Fourier transform of the autocorrelation function of the process in the ... 
Universal spectral features of different classes of random diffusivity processes
Sposini, V.; Grebenkov, D.S.; Metzler, R.; Oshanin, G.; Seno, F. (20200626)Stochastic models based on random diffusivities, such as the diffusing diffusivity approach, are popular concepts for the description of nonGaussian diffusion in heterogeneous media. Studies of these models typically ...