Dual spaces of cadlag processes

Teemu Pennanen and Ari-Pekka Perkkiö

Stochastic Processes and their Applications, 2023, vol. 157, issue C, 69-93

Abstract: 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.

Keywords: Banach function space; Stochastic process; Topological dual; Optional projection (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2022.11.017

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