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 inStochastic processes and their applications Vol. 157; pp. 69 - 93
Main Authors Pennanen, Teemu, Perkkiö, Ari-Pekka
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2023
Subjects
Banach function space
Optional projection
Stochastic process
Topological dual
Topological dual
46E30
Banach function space
Optional projection
60G07
Stochastic process
46N30
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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