Dual spaces of cadlag processes

Teemu Pennanen; Ari-Pekka Perkkio

doi:10.1016/j.spa.2022.11.017

Dual spaces of cadlag processes

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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 L ^p 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.

Original language	English
Pages (from-to)	69-93
Number of pages	25
Journal	Stochastic Processes and Their Applications
Volume	157
Early online date	12 Dec 2022
DOIs	https://doi.org/10.1016/j.spa.2022.11.017
Publication status	Published - 1 Mar 2023

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AB - 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 L p 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.

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JO - Stochastic Processes and Their Applications

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Dual spaces of cadlag processes

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