On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case

Abstract In this paper, we investigate the propagation of weak representation property (WRP) to an independently enlarged filtration. More precisely, consider $${\mathbb {F}}$$ F -semimartingale X possessing WRP with respect and {H}}$$ H Y . Assuming that are independent, show {G}}$$ G $$Z=(X,Y)$$ Z = ( X , Y ) has , where {G}}:={\mathbb {F}}\vee {\mathbb : ∨ our setting, may have simultaneous jump-times. Furthermore, their jumps charge same predictable times. This generalizes all available results about filtrations.