Large deviations for nonuniformly hyperbolic systems

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Homogenization for deterministic maps and multiplicative noise (2013, background): “Precise statements about the validity of the WIP and LDP can be found in [20, 21, 22].”
Inequalities and limit theorems for weakly dependent sequences (2013, methodology): “Inequality (a) may be applied to some dynamical systems with hyperbolicity, as shown by Melbourne and Nicol (2008). Inequality (b) can be improved if the strong mixing coefficients are defined by (2.”
Martingale–coboundary decomposition for families of dynamical systems (2016, methodology): “11 The moment estimates for p ≥ 2 were first obtained in [44] and the results for p < 2 are due to [22, 30].”
Smooth approximation of stochastic differential equations (2014, background): “1 makes essential use of the fact that v ∈ L∞ [26, 34, 38].”