We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for any other initialization, the difference of the two processes converges to zero almost surely. Under some mild conditions on the corresponding recursive map, without any condition on the driving sequence, we show the strong stability of iterations. Several applications are surveyed such as stochastic approximation and queuing. Furthermore, new results are deduced for Langevin-type iterations with dependent noise and for multitype branching processes.

翻译：我们重新审视由迭代随机函数生成的过程，该过程由一个平稳且遍历的序列驱动。如果存在随机初始化，使得该过程是平稳和遍历的，并且对于任何其他初始化，两个过程的差异几乎肯定收敛于零，则称这样的过程是强稳定的。在对应的递归地图上施加一些温和的条件，而无需对驱动序列进行任何条件，我们展示了遍历的强稳定性。我们概述了多个应用，例如随机逼近和排队。此外，新的结果可以推导出具有相关噪声的Langevin型迭代和多类型分支过程的结果。