Imajkin, V. M.; Komech, A. I. On large deviations of solutions of nonlinear stochastic equations. (Russian. English summary) Zbl 0675.60022 Tr. Semin. Im. I. G. Petrovskogo 13, 177-196 (1988). The large deviations principle is established for solutions of nonlinear partial stochastic differential equations \[ u(t,x)=\Delta_ xu(t,x)- f(u(t,x))+\epsilon w(t,x),\quad \epsilon \to 0. \] The result is a nontrivial analogue of the finite-dimensional theorems of A. D. Ventcel’ and M. I. Freídlin [Usp. Mat. Nauk 25, No.1(151), 3- 55 (1970; Zbl 0291.34042); English translation in Russ. Math. Surveys 25, No.1, 1-55 (1970)]. Reviewer: A.Yu.Veretennikov Cited in 1 ReviewCited in 1 Document MSC: 60F10 Large deviations 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:large deviations; partial stochastic differential equations Citations:Zbl 0291.34042 PDFBibTeX XMLCite \textit{V. M. Imajkin} and \textit{A. I. Komech}, Tr. Semin. Im. I. G. Petrovskogo 13, 177--196 (1988; Zbl 0675.60022)