Related papers: Analysis of Stochstic Evolution
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size…
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on…
The two-variable Langevin equations, modeling the Brownian motion of a particle moving in a potential and leading to the Maxwell-Boltzmann distribution of the corresponding Fokker-Planck equation, are shown to give rise to types of…
Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market…
The dynamics of generic stochastic Lotka-Volterra (discrete logistic) systems of the form \cite{Solomon96a} $w_i (t+1) = \lambda(t) w_i (t) + a {\bar w (t)} - b w_i (t) {\bar w(t)}$ is studied by computer simulations. The variables $w_i$,…
Recently, we developed a theory of a geometrically growing system. Here we show that the theory can explain some phenomena of power-law distribution including classical demographic and economic and novel pandemic instances, without…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
The Generalized Lotka Voltera (GLV) formalism has been introduced in order to explain the power law distributions in the individual wealth (w_i (t)) (Pareto law) and financial markets returns (fluctuations) (r) as a result of the…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…
We present a kinetic approach to the formation of urban agglomerations which is based on simple rules of immigration and emigration. In most cases, the Boltzmann-type kinetic description allows to obtain, within an asymptotic procedure, a…
Apparently random events in nature often reveal hidden patterns when analysed using diverse and robust statistical tools. Power-law distributions, for example, project diverse natural phenomenon, ranging from earthquakes1 to heartbeat…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
Present human languages display slightly asymmetric log-normal (Gauss) distribution for size [1-3], whereas present cities follow power law (Pareto-Zipf law)[4]. Our model considers the competition between languages and that between cities…
The evolution of urban landscapes is rapidly altering the surface of our planet. Yet, our understanding of the urbanisation phenomenon remains far from complete. A fundamental challenge is to describe spatiotemporal changes in the built…
This study investigates the emergence of power-law and other concentrated distributions through a feedback loop model in crowd interactions. Agents act by their response functions to observations and external forces, while observations…
Several problems arising in Economics and Finance are analyzed using concepts and quantitative methods from Physics. Here is the abridged abstact: Chapter 1: By analogy with energy, the equilibrium probability distribution of money must…
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…