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 



I would like to express my deepest gratitude to David B. Applebaum for all his advice, comments and suggestions that contributed to improve this work. I would also like to thank the referees of the paper for their careful reading and helpful suggestions. Thanks are also to both the School of Mathematics and Statistics (SoMaS) of The University of Sheffield and the Office of International Affairs and External Cooperation (OAICE) of The University of Costa Rica for providing financial support.


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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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