Stochastic process with ultraslow convergence to a Gaussian: The truncated Levy flight

We introduce a class of stochastic process, the truncated Levy flight (TLF), in which the arbitrarily large steps of a Levy 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 Levy and a Gaussian regime, and that the crossover carries information about the relevant parameters of the underlying stochastic process