It is shown that for sums of functionals of digits in continued fraction expansion the Kolmogorov-Feller weak laws of large numbers and the Khinchine-Lévy-Feller-Raikov characterization of the domain of attraction of the normal law hold.

Рассматривается классическая проблема больших уклонений для сумм случайных величин, заданных на состояниях однородной цепи Мар кова с конечным фазовым пространством. Устанавливается точная асим птотика для вероятностей больших уклонений порядка О [у/и). Доказа тельство основано на применении нового типа локальной теоремы. Ключевые слова и фразы: сопряженное распределение, локальная теорема, возмущение спектра, монотонная ^-аппроксимация.

It is shown that functionals of digits in continued fraction expansion satisfy either the DeMoivre-Gnedenko or the Shepp-Stone limit theorems if and only if their marginals are in the domain of attraction of the normal law.

Marcinkiewicz laws of large numbers for ϕ-mixing strictly stationary sequences with r-th moment barely divergent, 0 < r < 2, are established. For this dependent analogs of the Lévy-Ottaviani-Etemadi and Hoffmann-Jørgensen inequalities are revisited.

For a nonnegative strictly stationary random sequence satisfying the``minimal'' dependence condition necessary and sufficient conditions for the relative stability are found. As an application the well-known Khinchine stability result for i.i.d. random variables is proved for uniformly strong mixing sequences. AcademicPress AMS 1991 subject classification: 60F05; 60G10.