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Martingale spaces and representations under absolutely continuous changes of probability. (English) Zbl 07126977
Summary: 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.
MSC:
60G07 General theory of stochastic processes
60G44 Martingales with continuous parameter
60H05 Stochastic integrals
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