双指标非交换鞅的收敛性和不等式
CONVERGENCE AND INEQUALITIES OF TWO-PARAMETER NONCOMMUTATIVE MARTINGALES

本文研究了双指标非交换鞅的收敛性和不等式问题. 利用非交换代数和单指标鞅的方法, 获得了双指标Lp-有界鞅(1 ≤ p ≤ ∞) 的收敛性, L1-收敛性和一致可积的关系; 推广了双指标非交换鞅的两个不等式, 即Burkholder-Gundy 不等式和强鞅的Davis 不等式.
In this paper, we discuss the convergence and inequalities of two-parameter noncommutative martingales. By using noncommutative algebra and one-paremeter martingales methods, we have the convergence of Lp-bounded martingales(1 ≤ p ≤ ∞), the relation between L1-convergence and uniformly integrability of Lp-bounded martingales. And we generalize two inequalities of two-parameter noncommutative martingales, i.e., Burkholder-Gundy inequality and Davis's inequality for strong martingales