Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy 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 $n\approx {10}^4$ in contrast to $n\approx 10$ 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.