Self-similar stochastic models with stationary increments for symmetric space-time fractional diffusion
An approach to develop stochastic models for studying anomalous diffusion is proposed. In particular, in this approach the stochastic particle trajectory is based on the fractional Brownian motion but, for any realization, it is multiplied by an independent random variable properly distributed. The resulting probability density function for particle displacement can be represented by an integral formula of subordination type and, in the single-point case, it emerges to be equal to the solution of the spatially symmetric space-time fractional diffusion equation. Due to the fractional Brownian motion, this class of stochastic processes is self-similar with stationary increments in nature and uniquely defined by the mean and the auto-covariance structure analogously to the Gaussian processes. Special cases are the time-fractional diffusion, the space-fractional diffusion and the classical Gaussian diffusion.
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Pagnini G. (Physica A: Statistical Mechanics and its Applications, 2014-12-31)In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to ...
The M-Wright function as a generalization of the Gaussian density for fractional diffusion processes Pagnini G. (Fractional Calculus and Applied Analysis, 2013-12-31)The leading role of a special function of the Wright-type, referred to as M-Wright or Mainardi function, within a parametric class of self-similar stochastic processes with stationary increments, is surveyed. This class ...
Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion D’Ovidio M.; Vitali S.; Sposini V.; Sliusarenko O.; Paradisi P.; Castellani G.; Pagnini G. (Fractional Calculus and Applied Analysis, 2018-10-25)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 centre-of-mass ...