In a fully general setting, we study the relation between martingale spaces under two locally absolutely continuous probabilities and prove that the martingale representation property (MRP) is always stable under locally absolutely continuous changes of probability. Our approach relies on minimal requirements, is constructive and, as shown by a simple example, enables us to study situations which cannot be covered by the existing theory.
"Martingale spaces and representations under absolutely continuous changes of probability." Electron. Commun. Probab. 24 1 - 13, 2019. https://doi.org/10.1214/19-ECP253