Measurability of semimartingale characteristics with respect to the probability law

Ariel Neufeld and Marcel Nutz

Stochastic Processes and their Applications, 2014, vol. 124, issue 11, 3819-3845

Abstract: 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 (BP,C,νP) 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.

Keywords: Semimartingale characteristics; Semimartingale property; Doob–Meyer decomposition (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (27)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:11:p:3819-3845

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DOI: 10.1016/j.spa.2014.07.006

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