arXiv subjects

Luc Tri Tuyen

Publications and source records attributed to Luc Tri Tuyen.

2 recordsLinked to original sources

arXiv2026

On strong law of large numbers for weakly stationary $φ$-mixing set-valued random variable sequences

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.

math.PR↗

arXiv2024

A representation theorem for set-valued submartingales

The integral representation theorem for martingales has been widely used in probability theory. In this work, we propose and prove a general representation theorem for a class of set-valued submartingales. We also extend the stochastic integral representation for non-trivial initial set-valued martingales. Moreover, we show that this result covers the existing ones in the literature for both degenerated and non-degenerated set-valued martingales.

math.PR↗