For a large class of non-uniformly hyperbolic diffeomorphisms, we prove stochastic stability under small random noise: the unique stationary probability measure of the Markov chain converges to the Sinai–Ruelle–Bowen measure of the unperturbed attractor when the noise level tends to zero.
Cite this article
Michael Benedicks, Marcelo Viana, Random perturbations and statistical properties of Hénon-like maps. Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 5, pp. 713–752DOI 10.1016/J.ANIHPC.2004.10.013