arXiv subjects

Ph . Barbe

Publications and source records attributed to Ph . Barbe.

2 recordsLinked to original sources

arXiv2006

Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments

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 distribution of the maxima of the random walk generated by F. An application to ruin probabilities is developed.

math.PR↗

arXiv2006

Asymptotic expansions for distributions of compound sums of light subexponential random variables

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 of a Poisson and geometric number of summands serve as an illustration of the main result. Complete calculations are done for a Weibull distribution, with which we derive, as examples and without any difficulties, 7 terms expansions.

math.PR↗