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Dual spaces of cadlag processes

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  • Pennanen, Teemu
  • Perkkiö, Ari-Pekka

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.

Suggested Citation

  • Pennanen, Teemu & Perkkiö, Ari-Pekka, 2023. "Dual spaces of cadlag processes," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 69-93.
    • Handle: RePEc:eee:spapps:v:157:y:2023:i:c:p:69-93
    DOI: 10.1016/j.spa.2022.11.017
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    1. Pennanen, Teemu & Perkkiö, Ari-Pekka, 2018. "Convex integral functionals of regular processes," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1652-1677.
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