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Existence of Continuous and Càdlàg Versions for Cylindrical Processes in the Dual of a Nuclear Space

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  • C. A. Fonseca-Mora

    (Universidad de Costa Rica)

Abstract

Let $$\Phi $$ Φ be a nuclear space and let $$\Phi '_{\beta }$$ Φ β ′ denote its strong dual. In this paper, we introduce sufficient conditions for a cylindrical process in $$\Phi '$$ Φ ′ to have a version that is a $$\Phi '_{\beta }$$ Φ β ′ -valued continuous or càdlàg process. We also establish sufficient conditions for the existence of such a version taking values and having finite moments in a Hilbert space continuously embedded in $$\Phi '_{\beta }$$ Φ β ′ . Finally, we apply our results to the study of properties of cylindrical martingales in $$\Phi '$$ Φ ′ .

Suggested Citation

  • C. A. Fonseca-Mora, 2018. "Existence of Continuous and Càdlàg Versions for Cylindrical Processes in the Dual of a Nuclear Space," Journal of Theoretical Probability, Springer, vol. 31(2), pages 867-894, June.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:2:d:10.1007_s10959-016-0726-0
    DOI: 10.1007/s10959-016-0726-0
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    References listed on IDEAS

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    1. Bojdecki, Tomasz & Talarczyk, Anna, 2005. "Particle picture approach to the self-intersection local time of density processes in," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 449-479, March.
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