Related papers: Analysis of Stochstic Evolution
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
We present a possible approach to measuring inequality in a system of coupled Fokker-Planck-type equations that describe the evolution of distribution densities for two populations interacting pairwise due to social and/or economic factors.…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-M\'ezard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes,…
In this study, we investigate the statistical properties of the returns and the trading volume. We show a typical example of power-law distributions of the return and of the trading volume. Next, we propose an interacting agent model of…
We study unit-level expenditure on consumption across multiple countries and multiple years, in order to extract invariant features of consumption distribution. We show that the bulk of it is lognormally distributed, followed by a power law…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the…
The law of proportionate growth simply states that the time dependent change of a quantity $x$ is proportional to $x$. Its applicability to a wide range of dynamic phenomena is based on various assumptions for the proportionality factor,…
Here we postulate three laws which form a mathematical framework to capture the essence of Darwinian evolutionary dynamics. The second law is most quantitative and is explicitly expressed by a unique form of stochastic differential…
With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems from data. Despite the wide occurrences of non-Gaussian…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
We study the evolution leading to (or regressing from) a large fluctuation in a Statistical Mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$…
The diffusion of ideas and language in society has conventionally been described by S-shaped models, such as the logistic curve. However, the role of sub-exponential growth -- a slower-than-exponential pattern known in epidemiology -- has…
We study the probability distribution of the value of geometric Brownian motion at the stochastic observation time. It is known that the exponentially distributed observation time yields the distribution called the double Pareto…
This work develops a comprehensive mathematical theory for a class of stochastic processes whose local regularity adapts dynamically in response to their own state. We first introduce and rigorously analyze a time-varying fractional…
A mean-field like stochastic evolution equation with growth and reset terms (LGGR model) is used to model wealth distribution in modern societies. The stationary solution of the model leads to an analytical form for the density function…
We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in…