@article{FroylandGTQuas14,
  author={Gary Froyland and Cecilia Gonz\'alez-Tokman and Anthony Quas},
  title={{Stability and approximation of random invariant densities for Lasota--Yorke map cocycles}},
  journal={Nonlinearity},
  volume={27},
  number={4},
  pages={647},
  url={http://stacks.iop.org/0951-7715/27/i=4/a=647},
  year={2014},
  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.}
}