## The Annals of Probability

### Stability of perpetuities

#### Abstract

For a series of randomly discounted terms we give an integral criterion to distinguishbetween almost-sure absolute convergence and divergence in probability to $\infty$, these being the only possible forms of asymptotic behavior. This solves the existence problem for a one-dimensional perpetuity that remains from a 1979 study by Vervaat, and yields a complete characterization of the existence of distributional fixed points of a random affine map in dimension one.

#### Article information

Source
Ann. Probab., Volume 28, Number 3 (2000), 1195-1218.

Dates
First available in Project Euclid: 18 April 2002

https://projecteuclid.org/euclid.aop/1019160331

Digital Object Identifier
doi:10.1214/aop/1019160331

Mathematical Reviews number (MathSciNet)
MR1797309

Zentralblatt MATH identifier
1023.60037

Subjects

#### Citation

Goldie, Charles M.; Maller, Ross A. Stability of perpetuities. Ann. Probab. 28 (2000), no. 3, 1195--1218. doi:10.1214/aop/1019160331. https://projecteuclid.org/euclid.aop/1019160331

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