Large deviations for expanding transformations with additive white noise (Q1573788)

The authors derive level-2 large deviations bounds for empirical measures of processes having the form \(V_n=(X_n,\xi_n,\xi_{n+1})\), \(n\geq 0\), where \(\xi_1,\xi_2,\dots\) are i.i.d. random variables and \(X_n=T^n(X_0)\) with \(T\) being an expanding transformation on \(M.\) As in other papers on the subject [see, for instance, \textit{Yu. Kifer}, Trans. Am. Math. Soc. 321, No.~2, 505-524 (1990; Zbl 0714.60019)] this is done with respect to a probability measure on \(M\) which is a Gibbs measure for \(T\) corresponding to Hölder continuous function. The method is a combination of the Donsker-Varadhan approach and the thermodynamic formalism machinery.