Limit theorems for Markov processes in a rapidly changing random environment

Markov processes are considered in a rapidly changing random environment; the asymptotic behavior of the distribution for the number of nonappearing states is investigated. A limit theorem is obtained which enables us to approximate the distribution of the number of particles of a birth-and-death branching process in a rapidly changing environment by the limit distributions of an ordinary birth-and-death branching process.
Bibliography: 12 titles.