Levy flights

for some h, 0 < h < 2.

The jumps in a Levy flight are distributed according to a power law, that is,

Prob(Y > u) = u-h,

Levy flights have long tails, that is, although there are fewer long jumps than short jumps, the rate at which the number of long jumps decreases is much slower than for normal distributions.

Pictured here are the far right sides (the tails) of three hyperbolic distributions, for h = 0.5, h = 1.0, and h = 1.5, and the normal distribution for comparison.

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