Аннотация:
Necessary and sufficient conditions for the almost sure convergence of a series of autoregressive sequences in separable Banach spaces are studied. As an application of the obtained results, the condition for the admissible shift of a zero-mean Gaussian Markov measure is considered.
Ключевые слова:Autoregressive sequences, almost sure convergence of random series, summability theory, Gaussian Markov sequences, continuity and singularity of probabilistic measures.