Generation of Levy walk points

[Chegde8]

Hi,

Forgive me if this is a naive question.
In levywalk_gen.m you use Generalized Pareto Distribution to obtain Levy distributed points to generate a Levy walk. Is this correct?
If so, could you please point me to literature which states that the generalized pareto distribution can be used to obtain a Levy walk?
I am a little confused on how Levy walks can be generated. This link states that a Gaussian distribution can also be used: http://andreweckford.blogspot.com/2011/05/generating-levy-random-variables-from.html

Any pointers which will help me understand how Levy Walks can be generated is greatly appreciated.

Thanks!