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Motivated by applications to insurance mathematics, we prove someheavy-traffic limit theorems for process which encompass the fractionallyintegrated random walk as well as some FARIMA processes, when the innovationsare in the domain of attraction of a nonGaussian stable distribution.

Ruin probabilities in tough times - Part 1 - Heavy-traffic approximation  for fractionally integrated random walks in the domain of attraction of a  nonGaussian stable distribution