Abstract.
Considering the ordered convex cone \(\cal{S}\) of all positive right continuous supermartingales, we give a complete description of its dual. Also we study quasi-boundedness, quasi-continuity ans substractivity in \(\cal{S}\), proving that: the universally quasi-bounded potentials are exactly the potentials of class (D), the quasi-continuous potentials are exactly the regular potentials of class (D), and the substractible elements are exactly the local martingales.
Keywords: supermantigale, increasing process, (predictable) stopping time, Riesz decomposition property, duality
Mathematics Subject Classification (2000):
- 60Gxx
- 60Hxx
- 60Jxx
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© 2003 Springer-Verlag Berlin/Heidelberg
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Grecea, V. (2003). Duality and quasy-continuity for supermartingales. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVI. Lecture Notes in Mathematics, vol 1801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36107-7_19
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DOI: https://doi.org/10.1007/978-3-540-36107-7_19
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00072-3
Online ISBN: 978-3-540-36107-7
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