We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage...

We model the time series of the S&P500 index by a combined process, the AR+GARCH process, where AR denotes the autoregressive process which we use to account for the short-range correlations in the index changes and GARCH denotes the generalized autoregressive conditional heteroskedastic process...

We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy distribution. For both (i) and (ii), we find that due to the...

We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the...

We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U. S. economy over a period of four years. For all companies we find that: (i) the probability density function of intertrade times may be fit by a Weibull...

One particular practical problem in oil recovery is to predict the time to breakthrough of a fluid injected in one well and the subsequent decay in the production rate of oil at another well. Because we only have a stochastic view of the distribution of rock properties we need to predict the...

We present a scaling Ansatz for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for (i) the effect of the finite size of the system, and (ii) the dependence of this distribution on the site occupancy probability p. We present...

We analyze the fluctuations in the gross domestic product (GDP) of 152 countries for the period 1950--1992. We find that (i) the distribution of annual growth rates for countries of a given GDP decays with ``fatter'' tails than for a Gaussian, and (ii) the width of the distribution scales as a...