A steady result for large deviation in SDE with an application (Q2767421)

A steady property of large deviation for a perturbed stochastic differential equation is investigated. The author shows that appropriate perturbations to the drift term do not alter the large deviation property for a kind of degenerate diffusion processes, originated from the conservation law equations with random perturbation method. This work generalises the result of \textit{T.-S. Chiang} and \textit{S.-J. Sheu} [Stochastic Anal. Appl. 15, No. 1, 31-50 (1997; Zbl 0873.60013)] so that the discontinuities on the drift term can also appear as hypersurface. The proof is similar to that of \textit{M. I. Freidlin} and \textit{A. D. Wentzell} [``Random perturbation of dynamical systems'' (1998; Zbl 0922.60006)], which is based on the Girsanov theorem and Chebyshev's inequality. The result is applied to a degenerate diffusion process with drift jumping on a hypersurface.