Stability of perpetuities

• 成果类型: Article
• 署名作者: Goldie, CM; Maller, RA
• 署名单位: University of Sussex; University of Western Australia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 1195-1218
• 关键词: hoares selection algorithm; stationary coefficients

摘要

For a series of randomly discounted terms we give an integral criterion to distinguish between almost-sure absolute convergence and divergence in probability to infinity, 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.