Pointwise Properties of Martingales with Values in Banach Function Spaces
Mark Veraar (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Ivan Yaroslavtsev (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
In this paper we consider local martingales with values in a UMD Banach function space. We prove that such martingales have a version which is a martingale field. Moreover, a new Burkholder–Davis–Gundy type inequality is obtained.