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Stochastic resetting by a random amplitude
(2021-05-18)
Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting ...
Exact distributions of the maximum and range of random diffusivity processes
(2021-02-09)
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 first-passage time distributions for three random diffusivity models
(2021-01-04)
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, ...
Universal spectral features of different classes of random diffusivity processes
(2020-06-26)
Stochastic models based on random diffusivities, such as the diffusing- diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically ...
Single-trajectory spectral analysis of scaled Brownian motion
(2019-06)
A standard 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 ...
Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
(2019-02)
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite ...
Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers
(2018-10-18)
The emerging diffusive dynamics in many complex systems shows a
characteristic crossover behaviour from anomalous to normal diffusion which
is otherwise fitted by two independent power-laws. A prominent example for
a ...
Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
(2018-04)
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 ...