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

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Scaling in the Norwegian stock market (2000, background): “A very promising approach with respect to its application to mathematical nance [24], is the truncated L evy distribution [1,26,27].”
Physical pictures of transport in heterogeneous media: Advection‐dispersion, random‐walk, and fractional derivative formulations (2002, background): “For truncated Lévy distributions it is known that their scaling behaviors in time pertain up to relatively large times [Mantegna and Stanley, 1994, 1995].”
First exit times for Lévy-driven diffusions with exponentially light jumps. (2007, background): “The problem was first considered by Mantegna and Stanley in [19] and Koponen [17].”