Strong stochastic stability of multimodal Collet–Eckmann maps

A multimodal Collet–Eckmann map is a multimodal interval map satisfying the Collet–Eckmann condition, and strong stochastic stability means stability of its statistical behaviour under small random perturbations. Strong stochastic stability conjecture. Multimodal Collet–Eckmann maps are strongly stochastically stable. Tsujii's result on weak stochastic stability gives evidence in this direction, while it is possible that the Collet–Eckmann condition can be replaced by a weaker growth condition.