Abstract
Consider the perpetuity equation , where and on the right-hand side are independent. The Kesten–Grincevičius–Goldie theorem states that if , , and , then . Assume that for some , and consider two cases (i) , ; (ii) , for all . We show that under appropriate additional assumptions on the asymptotic holds, where is a nonconstant slowly varying function. We use Goldie’s renewal theoretic approach.
Citation
Péter Kevei. "A note on the Kesten–Grincevičius–Goldie theorem." Electron. Commun. Probab. 21 1 - 12, 2016. https://doi.org/10.1214/16-ECP9
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