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arXiv · 1212.2247

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles

Gary Froyland·Cecilia González-Tokman·Anthony Quas
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Abstract

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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Gary Froyland, Cecilia González-Tokman, Anthony Quas. 2012-12-10. Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. https://arxiv.org/abs/1212.2247

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