Related papers: Multiplicative processes and power laws

In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate…

In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in…

What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…

Science in the 21st century seems to be governed by novel approaches involving interdisciplinary work, systemic perspectives and complexity theory concepts. These new paradigms force us to leave aside our elder mechanistic approaches and…

In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous…

We study the large-time asymptotic of renewal-reward processes with a heavy-tailed waiting time distribution. It is known that the heavy tail of the distribution produces an extremely slow dynamics, resulting in a singular large deviation…

Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…

The problem of sums of independent, identically distributed random variables with stretched-exponential tails exhibits a dynamical phase transition and has recently reemerged in the context of active transport and condensation phenomena. We…

We derive an analytical approximation to the probability distribution function (pdf) for the response of Mathieu's equation under parametric excitation by a random process with a spectrum peaked at the main resonant frequency, motivated by…

The aftershock productivity law, first described by Utsu in 1970, is an exponential function of the form K=K0.exp({\alpha}M) where K is the number of aftershocks, M the mainshock magnitude, and {\alpha} the productivity parameter. The Utsu…

The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Considered the second most fundamental empirical law after the Gutenberg-Richter relationship, the power law…

In a recent Nature paper, Gabaix et al. \cite{Gabaix03} presented a theory to explain the power law tail of price fluctuations. The main points of their theory are that volume fluctuations, which have a power law tail with exponent roughly…

We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…

We consider a system of $N$ particles on the real line that evolves through iteration of the following steps: 1) every particle splits into two, 2) each particle jumps according to a prescribed displacement distribution supported on the…

We consider an ergodic process on finitely many states, with positive entropy. Our first main result asserts that the distribution function of the normalized waiting time for the first visit to a small (i.e., over a long block) cylinder set…

We study the situations when the solution to a weighted stochastic recursion has a power law tail. To this end, we develop two complementary approaches, the first one extends Goldie's (1991) implicit renewal theorem to cover recursions on…

Power-law type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constrains that limit the power-law range for the distributions…

A simple fragmentation model is introduced and analysed. We show that, under very general conditions, an effective power law for the mass distribution arises with realistic exponent. This exponent has a universal limit, but in practice the…