Related papers: On Rational Bubbles and Fat Tails
We study the formation of high energy tails in a one-dimensional kinetic model for granular gases, the so-called Inelastic Maxwell Model. We introduce a time- discretized version of the stochastic process, and show that continuous time…
We define a financial bubble as a period of unsustainable growth, when the price of an asset increases ever more quickly, in a series of accelerating phases of corrections and rebounds. More technically, during a bubble phase, the price…
A family of wave packets with power law tails are employed to analyze the long time dependence of the corresponding probability density. The densities, associated to packets for free particles in the one-dimensional space, with sufficiently…
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of…
A model of homogeneously driven dissipative system, consisting of a collection of $N$ particles that are characterized by only their velocities, is considered. Adopting a discrete time dynamics, at each time step, a pair of velocities is…
In proportional elections with open lists the excess of preferences received by candidates with respect to the list average is known to follow a universal lognormal distribution. We show that lognormality is broken provided preferences are…
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…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
This is an epistemological approach to errors in both inference and risk management, leading to necessary structural properties for the probability distribution. Many mechanisms have been used to show the emergence of fat tails. Here we…
Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…
We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
The present Letter, deals with the statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002) and Phys. Rev E {\bf 72}, 036108 (2005)], which predicts the probability distribution $p(E) \propto \exp_{\kappa} (-I)$, where, $I \propto \beta E…
Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes.…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
We investigate the shape of the Italian personal income distribution using microdata from the Survey on Household Income and Wealth, made publicly available by the Bank of Italy for the years 1977--2002. We find that the upper tail of the…
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,…
Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find…
Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven…
The distribution of returns in financial time series exhibits heavy tails. In empirical studies, it has been found that gaps between the orders in the order book lead to large price shifts and thereby to these heavy tails. We set up an…