α-Stable Lévy Process
A generalization of Brownian motion that permits arbitrarily large jumps, with increments following an α-stable distribution and exhibiting heavy tails. The parameter α ∈ (0, 2] controls tail thickness.
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At any positive generation time, the distribution produced by α-stable dynamics has a power-law tail with exponent α, whereas Brownian dynamics always remains light-tailed, a qualitative separation that does not depend on the specific target distribution or training details.
The α-stable Lévy process is a generalization of Brownian motion; Brownian motion corresponds to the stable process with α=2, and when α<2 the process allows arbitrarily large jumps and the jumps exhibit heavy-tailed characteristics.
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At any positive generation time, the distribution produced by α-stable dynamics has a power-law tail with exponent α, whereas Brownian dynamics always remains light-tailed, a qualitative separation that does not depend on the specific target distribution or training details.
50%UnverifiedThe α-stable Lévy process is a generalization of Brownian motion; Brownian motion corresponds to the stable process with α=2, and when α<2 the process allows arbitrarily large jumps and the jumps exhibit heavy-tailed characteristics.
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