Unifying constructions of martingales associated with processes increasing in the convex order, via Lévy and Sato sheets |
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| Authors: | Francis Hirsch Bernard Roynette Marc Yor |
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| Institution: | a Laboratoire d’Analyse et Probabilités, Université d’Évry - Val d’Essonne, Boulevard F. Mitterrand, F-91025 Évry Cedex, France;b Université Henri Poincaré, Institut de Mathématiques Elie Cartan, B.P. 239, F-54506 Vandoæuvre-lès-Nancy Cedex, France;c Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 Place Jussieu - Case 188, F-75252 Paris Cedex 05, France;d Institut Universitaire de France, France |
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| Abstract: | In this paper, we present a unified framework for our previous constructions of martingales with the same one-dimensional marginals as particular cases of processes increasing in the convex order. This framework encompasses our former uses of Lévy sheets, Sato sheets and self-decomposable laws. New examples of processes increasing in the convex order are also exhibited, but we do not know how to associate to them martingales with the same one-dimensional marginals. |
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