Analysis of Stochstic Evolution

Studies of collective human behavior in the social sciences, often grounded in details of actions by individuals, have much to offer `social' models from the physical sciences concerning elegant statistical regularities. Drawing on behavioral studies of social influence, we present a parsimonious, stochastic model, which generates an entire family of real-world right-skew socio-economic distributions, including exponential, winner-take-all, power law tails of varying exponent...

Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean. Empirical evidence of the validity of these laws has been found in many and diverse domains. Despite the numerous models proposed to explain the presence of Zipf's law, there is no consensus on how it originates from a microscopic process of i...

We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities providing a step toward defining a classification of the different levels of organization (the ``universality classes''). A rapid survey covers the Gaussian law, the power law and the stretched exponential distributions. The fascination for...

We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the frequencies of word occurrences in the language.

Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free behavior of the distribution of returns of different financial assets have been confirmed in a series of works. The existence of a Pareto-like distribution of the wealth of market participants has been connected with the scale-free distribut...

We consider an ideal closed stock market, in which 100 traders have economic activities. The assets of the traders change through buying and selling stocks. We simulate the assets under conservation of both total currency and total number of stocks. If the traders are identical, then the assets are distributed as a stationary Gaussian. When variety among the traders makes winners and losers, the asset distribution displays power law scaling such as the Pareto law. We discuss ...

In the present work, via computational simulation we study the statistical distribution of people versus number of steps acquired by them in a learning process, considering Darwin classical theory of evolution, i.e. competition, learning and survival for the fittest. We consider that learning ability is normally distributed. We found that the number of people versus step acquired by them in a learning process is given through a power law (N(n)=cn^-alpha). As competition, lear...

Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been demonstrated in various studies. The combination of the two just mentioned results, theoretical and experimental, supports strongly the scenario of biological evolution across different organisms. In the current Letter we explore in a general wa...

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 assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a 'fair' market, the wealth distribution among individual investors fulfills a power law. We then argue th...

We summarize a book under publication with his title written by the three present authors, on the theory of Zipf's law, and more generally of power laws, driven by the mechanism of proportional growth. The preprint is available upon request from the authors. For clarity, consistence of language and conciseness, we discuss the origin and conditions of the validity of Zipf's law using the terminology of firms' asset values. We use firms at the entities whose size distribution...