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



Let \(\Phi \) be a nuclear space and let \(\Phi '_{\beta }\) denote its strong dual. In this paper, we introduce sufficient conditions for a cylindrical process in \(\Phi '\) to have a version that is a \(\Phi '_{\beta }\)-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 \(\Phi '_{\beta }\). Finally, we apply our results to the study of properties of cylindrical martingales in \(\Phi '\).


Cylindrical stochastic processes Dual of a nuclear space Continuous and càdlàg versions Cylindrical martingales 

Mathematics Subject Classification (2010)

60B11 60G20 60G17 28C20 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Escuela de MatemáticaUniversidad de Costa RicaSan JoséCosta Rica

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