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Motivated by applications to insurance mathematics, we prove someheavy-traffic limit theorems for processes which encompass the fractionallydifferentiated random walk as well as some FARIMA processes, when theinnovations are in the domain of attraction of a nonGaussian stabledistribution.

Ruin probabilities in tough times - Part 2 - Heavy-traffic approximation  for fractionally differentiated random walks in the domain of attraction of a  nonGaussian stable distribution