We study the stochastic stability in the zero-noise limit from a quantitative point of view.
We consider smooth expanding maps of the circle perturbed by additive noise. We show that in this case the zero-noise limit has a quadratic speed of convergence, as suggested by numerical experiments and heuristics published by Lin, in 2005 (see [
We also consider the zero-noise limit from a quantitative point of view for piecewise expanding maps showing estimates for the speed of convergence in this case.
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Lipschitz approximation of a discontinuity, graphical representation of
Lipschitz approximation of a discontinuity, rescaling of the problem