Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy Flight

We introduce a class of stochastic process, the truncated L\'evy flight (TLF), in which the arbitrarily large steps of a L\'evy 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≈10⁴ in contrast to n≈10 for common distributions. We find a well-defined crossover between a L\'evy and a Gaussian regime, and that the crossover carries information about the relevant parameters of the underlying stochastic process.