Lasota-Yorke映射上循环的随机不变密度的稳定性和逼近
Stability and approximation of random invariant densities for Lasota-Yorke map cocycles
摘要：
本文建立了随机Lasota-Yorke映射的上圈在各种扰动下的随机绝对连续不变测度的稳定性。我们的随机映射族不需要接近固定映射，因此，我们的结果可以处理非常一般的驱动机制。我们考虑（i）通过卷积的扰动，（ii）扰动所产生的有限秩转移算子近似计划和（iii）静态扰动，扰动附近的上循环的Lasota-Yorke映射。前两个结果提供了一个严格的框架，随机acims的数值逼近使用基于傅立叶的方法和乌拉姆的方法，分别，我们也证明了这些计划的有效性。
英文摘要：
We establish stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota-Yorke maps under a variety of perturbations. Our family of random maps need not be close to a fixed map; thus, our results can handle very general driving mechanisms. We consider (i) perturbations via convolutions, (ii) perturbations arising from finite-rank transfer operator approximation schemes and (iii) static perturbations, perturbing to a nearby cocycle of Lasota-Yorke maps. The former two results provide a rigorous framework for the numerical approximation of random acims using a Fourier-based approach and Ulam's method, respectively; we also demonstrate the efficacy of these schemes.
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