Perpetuities with thin tails revisited

Hitczenko, Paweł; Wesołowski, Jacek

Ann. Appl. Probab., Tome 19 (2009) no. 1, p. 2080-2101 / Harvested from Project Euclid

Résumé

We consider the tail behavior of random variables R which are solutions of the distributional equation $R\stackrel{d}{=}Q+MR$ , where (Q, M) is independent of R and |M|≤1. Goldie and Grübel showed that the tails of R are no heavier than exponential and that if Q is bounded and M resembles near 1 the uniform distribution, then the tails of R are Poissonian. In this paper, we further investigate the connection between the tails of R and the behavior of M near 1. We focus on the special case when Q is constant and M is nonnegative.

Publié le : 2009-12-15
Classification: Perpetuity, stochastic difference equation, tail behavior, 60H25, 60E99

@article{1259158767,
     author = {Hitczenko, Pawe\l\ and Weso\l owski, Jacek},
     title = {Perpetuities with thin tails revisited},
     journal = {Ann. Appl. Probab.},
     volume = {19},
     number = {1},
     year = {2009},
     pages = { 2080-2101},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1259158767}
}

Hitczenko, Paweł; Wesołowski, Jacek. Perpetuities with thin tails revisited. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp.  2080-2101. http://gdmltest.u-ga.fr/item/1259158767/