2 citations · 5 across the 13 of their papers we have counts for
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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
Ph. Barbe, W. P. McCormick
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for processes which encompass the fractionally differentiated random walk as well as…
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
Ph. Barbe, W. P. McCormick
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for process which encompass the fractionally integrated random walk as well as some F…
Invariance principles for some FARIMA and nonstationary linear processes in the domain of a stable distribution
Ph. Barbe, W. P. McCormick
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The…
An extension of a logarithmic form of Cramer's ruin theorem to some FARIMA and related processes
Ph. Barbe, W. P. McCormick
Cramer's theorem provides an estimate for the tail probability of the maximum of a random walk with negative drift and increments having a moment generating function finite in a ne…
Veraverbeke's theorem at large - On the maximum of some processes with negative drift and heavy tail innovations
Philippe Barbe, Bill McCormick
Veraverbeke's (1977) theorem relates the tail of the distribution of the supremum of a random walk with negative drift to the tail of the distribution of its increments, or equival…
Asymptotic expansions for distributions of compound sums of light subexponential random variables
Ph . Barbe, W. P. McCormick, C. Zhang
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples…