Measurability of Semimartingale Characteristics with Respect to the Probability Law
نویسندگان
چکیده
Given a càdlàg process X on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let Psem be the set of all probability measures P under which X is a semimartingale. We construct processes (B , C, ν ) which are jointly measurable in time, space, and the probability law P , and are versions of the semimartingale characteristics of X under P for each P ∈ Psem. This result gives a general and unifying answer to measurability questions that arise in the context of quasi-sure analysis and stochastic control under the weak formulation.
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