Random evolution in a scheme of asymptotically small diffusion with Markov switchings
The subject of the paper is connected with the determination of the limit exponential generator for random evolution in an asymptotically small diffusion scheme using a small parameter of series and the solution to the singular perturbation problem for a uniformly ergodic Markov process. Previously, I. N. Sanov, N. V. Smirnov and D. Kramer studied the problem of determining the probability of large deviations of random quantities. Further, \textit{N. V. Smirnov} [Probability theory and mathematical statistics: Selected works (Russian). Moskow: Nauka (1970)] and \textit{A. N. Kolmogorov} [Basic concepts of probability theory (Russian). Moskow: Nauka (1974; Zbl 0278.60002)] found certain distributions of ``normal'' deviations.
scientific article; zbMATH DE number 6361206