Random perturbations of dynamical systems. Die Grundlehren der mathematischen Wissenschaften; 260.

From the reviews of the third edition:

“The celebrated work of Ventsel and Freidlin has proved to be a major contribution in this development, with their phenomenal text Random Perturbations of Dynamical Systems, now in its third edition, playing a unique role. ... The book under review has evolved since its first English edition was published in 1984, a translation from the Russian original of 1979. ... it will attract an ever growing population of applied mathematicians to the fascinating new frontier of stochastic dynamics.” (Hong Qian and Hao Ge, SIAM Review, Vol. 55 (3), 2013)