A note on stochastic integration with respect to optional semimartingales.
Kühn, Christoph, Stroh, Maximilian (2009)
Electronic Communications in Probability [electronic only]
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Kühn, Christoph, Stroh, Maximilian (2009)
Electronic Communications in Probability [electronic only]
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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.
Watanabe, Shinzo (2009)
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