11 citations · 26 across the 16 of their papers we have counts for
11 papers · 1 filter
A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values
Ph. Barbe, Miriam Isabel Seifert
We consider a real random variable X represented through a random pair of real random variables (R,T) and a deterministic function u as X=Ru(T). Under some additional assumptions,…
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…