On strong law of large numbers for weakly stationary $φ$-mixing set-valued random variable sequences
Abstract
In this paper we extend the notion of $φ$-mixing to set-valued random sequences that take values in the family of closed subsets of a Banach space. Several strong laws of large numbers for such $φ$-mixing sequences are stated and proved. Illustrative examples show that the hypotheses of the theorems are both natural and sharp.
Fields of Study & Subjects
Advanced Banach Space Theory
Probability and Statistical Research
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 14 January 2026
- Document type
- Preprint