Related papers: Probability distributions for one component equati…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
Proliferating cell populations at steady state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…
In this work, we consider diffusion-based molecular communication timing channels. Three different timing channels are presented based on three different modulation techniques, i.e., i) modulation of the release timing of the information…
The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
This paper studies the stability properties of stochastic differential equations subject to persistent noise (including the case of additive noise), which is noise that is present even at the equilibria of the underlying differential…
Stochastic bistable systems whose stationary distributions belong to the q-exponential family are investigated using two approaches: (i) the Langevin model subjected to additive and quadratic multiplicative noise, and (ii) the…
We consider stochastic model based on the linear stochastic differential equation with the linear relaxation and with the diffusion-like fluctuations of the relaxation rate. The model generates monofractal signals with the non-Gaussian…
We show that two dynamical systems exhibiting very different deterministic behaviours possess very similar stationary distributions when stabilized by a multiplicative Gaussian white noise. We also discuss practical aspects of numerically…
We discuss the influence of white noise on a generic dynamical finite-time-singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time-singularity and replaces it by a first-passage-time or…
Starting from the developed generalized point process model of $1/f$ noise (B. Kaulakys et al, Phys. Rev. E 71 (2005) 051105; cond-mat/0504025) we derive the nonlinear stochastic differential equations for the signal exhibiting 1/f^{\beta}$…
This study reports on the evolution of the probability distribution in the configuration space of the two-dimensional Toda system. The distribution is characterized by singularities, which predominantly take two forms: double-cusped…
We study the behavior of the spectra corresponding to quantum systems subjected to a contractive noise, i.e. the environment reduces the accessible phase space of the system, but the total probability is conserved. We find that the number…
We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former…
We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…
Nonlinear stochastic differential equations generating signals with 1/f spectrum have been used so far to describe socio-economical systems. In this paper we consider the motion of a Brownian particle in an inhomogeneous environment such…
We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability…