A new proof of Kellerer’s theorem
1 Laboratoire d’Analyse et Probabilités, Université d’Évry, Val d’Essonne, Boulevard F. Mitterrand, 91025 Évry Cedex, France
2 Institut Elie Cartan, Université Henri Poincaré, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France
Received: 21 June 2011
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
Mathematics Subject Classification: 60E15 / 60G44 / 60G48 / 60H10 / 35K15
Key words: Convex order / 1-martingale / peacock / Fokker-Planck equation
© EDP Sciences, SMAI, 2012