Given that financial series are poorly described by Gaussian distributions, how can the volatility behavior of such series be explained? Here we put forward a possible explanation to add the existing ones. We focus on a class of reduced variables that are independent and identically distributed....

This paper considers independently distributed stochastic processes that are also nonidentically distributed. We find that an identically distributed process with autocorrelations can be obtained from an independent, yet nonidentically distributed, random generator. Our approach is illustrated...

Based on the tick-by-tick stock prices from the German and American stock markets, we study the statistical properties of the distribution of the individual stocks and the index returns in highly collective and noisy intervals of trading, separately. We show that periods characterized by the...

We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to...

Increasing the number N of elements of a system typically makes the entropy to increase. The question arises on what particular entropic form we have in mind and how it increases with N. Thermodynamically speaking it makes sense to choose an entropy which increases linearly with N for large N,...

We introduce a general process designed to model stochastic systems in which the dependence of random variables is not through addition only but combined addition and subtraction with bounded ranges, and whose probabilistic factors have compact support. We show that, still retaining much of the...

Consider a sequence of Poisson random connection models (Xn,λn,gn) on Rd, where λn/nd→λ0 and gn(x)=g(nx) for some non-increasing, integrable connection function g. Let In(g) be the number of isolated vertices of (Xn,λn,gn) in some bounded Borel set K, where K has non-empty interior and...

Consider a sequence of independent Poisson point processes X1,X2,… with densities λ1,λ2,…, respectively, and connection functions g1,g2,… defined by gn(r)=g(nr), for r0 and for some integrable function g. The Poisson random connection model (Xn,λn,gn) is a random graph with vertex set...