The "Grundlehren der mathematischen Wissenschaften" is a series of comprehensive mathematical studies. This volume, numbered 260, is titled "Random Perturbations of Dynamical Systems" and is the second edition. It was originally published in Russian in 1979 and translated into English. The book focuses on the study of random perturbations of dynamical systems, particularly large deviations and their applications. It includes a detailed discussion of the theory of large deviations for stochastic processes, as well as the averaging principle and other related topics. The book also covers the behavior of random processes on large time intervals, the exit of a random process from a domain, and the stability of such processes under random perturbations. The content includes various asymptotic problems arising as the parameter characterizing the smallness of random perturbations converges to zero. The book is written for mathematicians but is also accessible to specialists in adjacent fields. It includes a detailed introduction, chapters on random perturbations, Gaussian perturbations, Markov processes, and stability under random perturbations, along with references and an index. The book is a comprehensive resource on the subject of random perturbations of dynamical systems, providing both theoretical and applied insights into the behavior of such systems under random influences.The "Grundlehren der mathematischen Wissenschaften" is a series of comprehensive mathematical studies. This volume, numbered 260, is titled "Random Perturbations of Dynamical Systems" and is the second edition. It was originally published in Russian in 1979 and translated into English. The book focuses on the study of random perturbations of dynamical systems, particularly large deviations and their applications. It includes a detailed discussion of the theory of large deviations for stochastic processes, as well as the averaging principle and other related topics. The book also covers the behavior of random processes on large time intervals, the exit of a random process from a domain, and the stability of such processes under random perturbations. The content includes various asymptotic problems arising as the parameter characterizing the smallness of random perturbations converges to zero. The book is written for mathematicians but is also accessible to specialists in adjacent fields. It includes a detailed introduction, chapters on random perturbations, Gaussian perturbations, Markov processes, and stability under random perturbations, along with references and an index. The book is a comprehensive resource on the subject of random perturbations of dynamical systems, providing both theoretical and applied insights into the behavior of such systems under random influences.