A discussion is presented of the effects of stochasticity in the decision-making of agents in the minority game. Both simulational and analytic results are reported and discussed for both additive and multiplicative noise. As a function of the ratio d of information dimension to number of agents...

We investigate a statistical ensemble of daily returns of n equities traded in United States financial markets. For each trading day of our database, we study the ensemble return distribution. We find that a typical ensemble return distribution exists in most of the trading days 1 with the...

Recent theoretical studies and extensive data analyses have revealed a common feature displayed by biological, social and technological networks: the presence of small world patterns. Here we analyse this problem by using several graphs obtained from one of the most common technological systems:...

We demonstrate that the Fokker–Planck equation can be generalized into a ‘fractional Fokker–Planck’ equation, i.e., an equation which includes fractional space differentiations, in order to encompass the wide class of anomalous diffusions due to a Lévy stable stochastic forcing. A...