The random record distributed v associated with a probability distribution mu can be written as a convolution series, nu = Sigma (infinity)(n=1)(n + 1)(-1)mu (*n). Various authors have obtained results on the behaviour of the tails nu((x, infinity)) as x --> infinity, using Laplace transforms and the associated Abelian and Tauberian theorems. Here me use Gelfand transforms and the Wiener-Levy-Glefand. Theorem to obtain expansions of the tails under moment conditions on mu. The results differ notably from those known for other convolution series.
The random record distributed v associated with a probability distribution mu can be written as a convolution series, nu = Sigma (infinity)(n=1)(n + 1)(-1)mu (*n). Various authors have obtained results on the behaviour of the tails nu((x, infinity)) as x --> infinity, using Laplace transforms and the associated Abelian and Tauberian theorems. Here me use Gelfand transforms and the Wiener-Levy-Glefand. Theorem to obtain expansions of the tails under moment conditions on mu. The results differ notably from those known for other convolution series.
Hahn; Wassmuth, Chemische Berichte, 1934, vol. 67, p. 696,702