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The unpredictability of chaotic nonlinear dynamics leads naturally tostatistical descriptions, including probabilistic limit laws such as thecentral limit theorem and large deviation principle. A key tool in theNagaev-Guivarc'h spectral method for establishing statistical limit theorems isa "twisted" transfer operator. In the abstract setting of Keller-Liverani weprove that derivatives of all orders of the leading eigenvalues andeigenprojections of the twisted transfer operators with respect to the twistparameter are stable when subjected to a broad class of perturbations. As aresult, we demonstrate stability of the variance in the central limit theoremand the rate function from a large deviation principle with respect todeterministic and stochastic perturbations of the dynamics and perturbationsinduced by numerical schemes. We apply these results to piecewise expandingmaps in one and multiple dimensions, including new convergence results for Ulamprojections on quasi-H\"older spaces.

Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps