Related papers: Asymmetric Anomalous Diffusion: an Efficient Way t…
We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic…
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider {\it strong anomalous} diffusion characterized by the moment behaviour $\langle x(t)^q \rangle \sim t^{q \nu(q)}$,…
The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail is reexamined from a fundamental statistical point of view making use of the division of particle orbits into waiting…
In this paper we analyze a coupling between the very large jumps in physical and operational times as applied to anomalous diffusion. The approach is based on subordination of a skewed Levy-stable process by its inverse to get two types of…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…
The origin of deterministic diffusion is a matter of discussion. We study the asymptotic distributions of the sums $y_n(x)=\sum_{k=0}^{n-1}\psi (x+k\alpha)$, where $\psi$ is a periodic function of bounded variation and $\alpha$ an…
We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…
Anomalous dynamics in which local perturbations spread faster than diffusion are ubiquitously observed in the long-time behavior of a wide variety of systems. Here, the manner by which such systems evolve towards their asymptotic…
This paper introduces a new methodology for detecting anomalies in time series data, with a primary application to monitoring the health of (micro-) services and cloud resources. The main novelty in our approach is that instead of modeling…
We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square…
We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the accumulated…
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination…
In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time and ensemble average mean squared displacement are remarkably different. The ensemble average diffusivity is…
We report a new accelerated diffusion phenomenon that is produced by a one-dimensional ran- dom walk in which the flight probability to one of the two directions (i.e., bias) oscillates dynam- ically in periodic, quasiperiodic, and chaotic…
Subordinated processes play an important role in modeling anomalous diffusion-type behavior. In such models the observed constant time periods are described by the subordinator distribution. Therefore, on the basis of the observed time…
This paper proposes a simple model of anomalous diffusion, in which a particle moves with the velocity field induced by a single "dipole" (a doublet or a pair of source and sink), whose moment is modulated randomly at each time step. A…
We consider the random walk of a particle in a two-dimensional self-affine random potential of Hurst exponent $H=1/2$ in the presence of an external force $F$. We present numerical results on the statistics of first-passage times that…
In a recent paper [2] the author introduced and investigated a random walk model similar to a model introduced in [1]. In these models the increment of the random walk depends on the complete past of the process. In this note I will point…
Processes involving bursts of activity separated by quiescent periods occur across diverse systems and scales. In human dynamics, these phenomena have been described by power-law inter-event time distributions, $P(t)\sim t^{-\alpha}$, with…