Dual spaces of cadlag processes

This article characterizes topological duals of spaces of cadlag processes. We extend functional analytic results of Dellacherie and Meyer that underlie many fundamental results in stochastic analysis and optimization. We unify earlier duality results on Lp and Orlicz spaces of cadlag processes and...

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Bibliographic Details
Published in:Stochastic processes and their applications 2023-03, Vol.157, p.69-93
Main Authors: Pennanen, Teemu, Perkkiö, Ari-Pekka
Format: Article
Language:English
Subjects:
Banach function space
Optional projection
Stochastic process
Topological dual
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Summary:This article characterizes topological duals of spaces of cadlag processes. We extend functional analytic results of Dellacherie and Meyer that underlie many fundamental results in stochastic analysis and optimization. We unify earlier duality results on Lp and Orlicz spaces of cadlag processes and extend them to general Fréchet functions spaces. In particular, we obtain a characterization of the dual of cadlag processes of class (D) in terms of optional measures of essentially bounded variation. When applied to regular processes, we extend (Bismut, 1978) on projections of continuous processes. More interestingly, our argument yields characterizations of dual spaces of regular processes.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2022.11.017