Simulations for Karlin random fields

We investigate the simulation methods for a large family of stable random fields that appear in recent literature, known as the Karlin stable set-indexed processes, including fractional L\'evy-Chenstov stable fields as special cases. Our methods exploit a new representation for Karlin stable set-indexed processes which facilitates efficient simulations, and we implement the standard procedure introduced by Asmussen and Rosinski (2001) by first decomposing the random fields into large-jump and small-jump parts, and simulating each part separately. Computational issues arise when passing from time-indexed processes to manifold-indexed ones, and our methods are adjusted accordingly.

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