2 citations · 2 across the 4 of their papers we have counts for
6 papers
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…
Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments
Ph . Barbe, W. P. McCormick, C. Zhang
Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail di…
Asympyotic expansions for infinite weighted convolutions of light subexponential distributions
Ph. Barbe, W. P. McCormick
We establish some asymptotic expansions for infinite weighted convolutions of distributions having light subexponential tails. Examples are presented, some showing that in order to…
Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications
Ph. Barbe, W. P. McCormick
We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are deve…