Martingales on noncompact manifolds : maximal inequalities and prescribed limits
R.W.R. Darling (1996)
Annales de l'I.H.P. Probabilités et statistiques
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Displaying similar documents to “Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps”
Martingales on noncompact manifolds : maximal inequalities and prescribed limits
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A new proof of Kellerer’s theorem
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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.