Abstract
In this note a simple proof of the equivalence of the predictable representation property of a martingale with respect to a filtration associated with an orthogonal martingale measure and the extremality of the underlying probability measure P is given. The representation property enables us to characterize all measures which are locally absolutely continuous with respect to P. We apply this to superprocesses and remark on a related property of the excursion filtration of the Brownian motion.
Supported by an EC-Fellowship under Contract No. ERBCHBICT930682 and a DFG-Fellowship.
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Overbeck, L. (1995). On the predictable representation property for superprocesses. In: Azéma, J., Emery, M., Meyer, P.A., Yor, M. (eds) Séminaire de Probabilités XXIX. Lecture Notes in Mathematics, vol 1613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094203
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DOI: https://doi.org/10.1007/BFb0094203
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