Stability of perpetuities
Charles M. Goldie and Ross A. Maller
Source: Ann. Probab. Volume 28, Number 3 (2000), 1195-1218.
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.
Primary Subjects: 60H25
Keywords: Distributional fixed point; perpetuity; random affine map; randomly discounted series
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1019160331
Mathematical Reviews number (MathSciNet):
MR1797309
Digital Object Identifier: doi:10.1214/aop/1019160331
Zentralblatt MATH identifier:
1023.60037
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