@article{SposiniMetzlerOshanin2019,
  author    = {Sposini, Vittoria and Metzler, Ralf and Oshanin, Gleb},
  title     = {Single-trajectory spectral analysis of scaled Brownian motion},
  series = {New Journal of Physics},
  volume    = {21},
  journal   = {New Journal of Physics},
  publisher = {Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics},
  address   = {Bad Honnef und London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab2f52},
  pages     = {16},
  year      = {2019},
  abstract  = {Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.},
  language  = {en}
}
@article{SposiniChechkinMetzler2018,
  author    = {Sposini, Vittoria and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {First passage statistics for diffusing diffusivity},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {52},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {4},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aaf6ff},
  pages     = {11},
  year      = {2018},
  abstract  = {A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law < r(2)(t)> similar or equal to Dt yet the distribution of particle displacements is strongly non-Gaussian. A central approach to describe this effect is the diffusing diffusivity (DD) model in which the diffusion coefficient itself is a stochastic quantity, mimicking heterogeneities of the environment encountered by the tracer particle on its path. We here quantify in terms of analytical and numerical approaches the first passage behaviour of the DD model. We observe significant modifications compared to Brownian-Gaussian diffusion, in particular that the DD model may have a faster first passage dynamics. Moreover we find a universal crossover point of the survival probability independent of the initial condition.},
  language  = {en}
}
@article{VitaliSposiniSliusarenkoetal.2018,
  author    = {Vitali, Silvia and Sposini, Vittoria and Sliusarenko, Oleksii and Paradisi, Paolo and Castellani, Gastone and Pagnini, Gianni},
  title     = {Langevin equation in complex media and anomalous diffusion},
  series = {Interface : journal of the Royal Society},
  volume    = {15},
  journal   = {Interface : journal of the Royal Society},
  number    = {145},
  publisher = {Royal Society},
  address   = {London},
  issn      = {1742-5689},
  doi       = {10.1098/rsif.2018.0282},
  pages     = {10},
  year      = {2018},
  abstract  = {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 as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian motion. To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modelling of velocity dynamics. The complexity of the medium is parametrized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particle's dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations.},
  language  = {en}
}
@article{SposiniChechkinSenoetal.2018,
  author    = {Sposini, Vittoria and Chechkin, Aleksei V. and Seno, Flavio and Pagnini, Gianni and Metzler, Ralf},
  title     = {Random diffusivity from stochastic equations},
  series = {New Journal of Physics},
  journal   = {New Journal of Physics},
  publisher = {Deutsche Physikalische Gesellschaft / Institute of Physics},
  address   = {Bad Honnef und London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/aab696},
  pages     = {1 -- 33},
  year      = {2018},
  abstract  = {A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential(Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.},
  language  = {en}
}
@misc{SposiniChechkinFlavioetal.2018,
  author    = {Sposini, Vittoria and Chechkin, Aleksei V. and Flavio, Seno and Pagnini, Gianni and Metzler, Ralf},
  title     = {Random diffusivity from stochastic equations},
  series = {New Journal of Physics},
  journal   = {New Journal of Physics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-409743},
  pages     = {33},
  year      = {2018},
  abstract  = {Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential(Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.},
  language  = {en}
}