Spaces of regular abstract martingales

Abstract

In [15,10], the authors introduced and studied the space M r of regular martingales on a vector lattice and the space M r of bounded regular martingales on a Banach lattice. In this note, we study these two spaces from the vector lattice point of view. We show, in particular, that these spaces need not be vector lattices. However, if the underlying space is order complete then M r is a vector lattice and M r is a Banach lattice under the regular norm.

Near-epoch dependence in Riesz spaces

“…Schaefer [17], Stoica [18,19] and Troitsky [21] considered the extension of the concepts of conditional expectation and martingales to Banach lattices. See [7,20,22] for some recent developments in this area. In 2004, Kuo, Labuschagne and Watson [9] generalized these concepts to vector lattices (Riesz spaces).…”