Document - Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion

2018

Journal article Open Access

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.

Mathematical Physics (math-ph) superposition FOS: Mathematics Statistical Mechanics (cond-mat.stat-mech) FOS: Physical sciences heterogeneous ensemble center of mass Ornstein-Uhlenbeck proce Center of mass Mathematics - Probability generalized grey Brownian motion Condensed Matter - Statistical Mechanics anomalous diffusion Ornstein-Uhlenbeck process Analysi Mathematical Physics non-autonomous stochastic differential equation randomly-scaled Gaussian proce fractional diffusion center of ma Probability (math.PR) Analysis Ornstein–Uhlenbeck process Applied Mathematics randomly-scaled Gaussian process

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 like variable corresponding to this ensemble is statistically equivalent to a process driven by a non-autonomous stochastic differential equation with time-dependent drift and a white noise. In particular, the time scaling and the density function of such variable are driven by the population of timescales and of noise amplitudes, respectively. Moreover, we show that this variable is equivalent in distribution to a randomly-scaled Gaussian process, i.e., a process built by the product of a Gaussian process times a non-negative independent random variable. This last result establishes a connection with the so-called generalized grey Brownian motion and suggests application to model fractional anomalous diffusion in biological systems.

Source: Fractional Calculus & Applied Analysis (Print) 21 (2018): 1420–1435. doi:10.1515/fca-2018-0074

Publisher: Bulgarian Academy of Sciences. Institute of Mathematics and Informatics, Sofia , Bulgaria

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@article{oai:it.cnr:prodotti:401213,
	title = {Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion},
	author = {D'Ovidio M. and Vitali S. and Sposini V. and Sliusarenko O. and Paradisi P. and Castellani G. and Pagnini G.},
	publisher = {Bulgarian Academy of Sciences. Institute of Mathematics and Informatics, Sofia , Bulgaria},
	doi = {10.1515/fca-2018-0074 and 10.48550/arxiv.1806.11351},
	journal = {Fractional Calculus \& Applied Analysis (Print)},
	volume = {21},
	pages = {1420–1435},
	year = {2018}
}