STOCHASTIC-PROCESS WITH ULTRASLOW CONVERGENCE TO A GAUSSIAN - THE TRUNCATED LEVY FLIGHT

We introduce a class of stochastic process, the truncated Lévy flight (TLF), in which the arbitrarily large steps of a Lévy flight are eliminated. We find that the convergence of the sum of n independent TLFs to a Gaussian process can require a remarkably large value of n-typically n104 in contrast to n10 for common distributions. We find a well-defined crossover between a Lévy and a Gaussian regime, and that the crossover carries information about the relevant parameters of the underlying stochastic process. © 1994 The American Physical Society.