Semimartingales in predictable random open sets
Wei-An Zheng (1982)
Séminaire de probabilités de Strasbourg
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Displaying similar documents to “The martingale problem for a class of pseudo differential operators.”
Semimartingales in predictable random open sets
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One way to represent the generator of a Markov process is given by pseudo differential operators. Above all this is due to the fact that the generator satisfies the so-called positive maximum principle (...).
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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.
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Richard Lechner (2013)
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We obtain a representation as martingale transform operators for the rearrangement and shift operators introduced by T. Figiel. The martingale transforms and the underlying sigma algebras are obtained explicitly by combinatorial means. The known norm estimates for those operators are a direct consequence of our representation.
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