On the convergence of series of autoregressive sequences in Banach spaces. (English) Zbl 1224.60094
Summary: 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 obtained.
MSC:
| 60G50 | Sums of independent random variables; random walks |
| 60G15 | Gaussian processes |
| 40C05 | Matrix methods for summability |
| 60G30 | Continuity and singularity of induced measures |
