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July 2000 Stability of perpetuities
Charles M. Goldie, Ross A. Maller
Ann. Probab. 28(3): 1195-1218 (July 2000). DOI: 10.1214/aop/1019160331

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.

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Charles M. Goldie. Ross A. Maller. "Stability of perpetuities." Ann. Probab. 28 (3) 1195 - 1218, July 2000. https://doi.org/10.1214/aop/1019160331

Information

Published: July 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1023.60037
MathSciNet: MR1797309
Digital Object Identifier: 10.1214/aop/1019160331

Subjects:
Primary: 60H25

Keywords: Distributional fixed point , perpetuity , random affine map , randomly discounted series

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 3 • July 2000
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