On some applicable versions of abstract large deviations theorems (Q1180575)

The author refines the large deviation result of \textit{P. Baldi} [Ann. Mat. Pura Appl., IV. Ser. 151, 161-177 (1988; Zbl 0654.60024)]. Namely, for a given exponentially tight family of subprobability measures \(\{\mu_ \varepsilon\}\) on a Banach space \(X\), suppose that \(X\) is a dense subspace of another Banach space \(Y\) and the induced family of measures \(\{\nu_ \varepsilon\}\) on \(Y\) satisfies appropriate conditions allowing to identify the rate function \(L_ Y\) for \(\{\nu_ \varepsilon\}\). Then \(\{\mu_ \varepsilon\}\) satisfies the large deviation principle (on \(X\)) with rate function \(L=L_ Y\circ I\), where \(I\) is an operator of natural embedding of \(X\) into \(Y\). This result is applied to investigate large deviation properties of some reaction- diffusion equations with quick random noise.