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Parametrix techniques and martingale problem for some degenerate Kolmogorov's equations

Abstract : We prove the uniqueness of the martingale problem associated to some degenerate operators. The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins (From Probability to Geometry, vol. in honor of J.M Bismut (2009)) to prove uniqueness of the martingale problem in the framework of non degenerated elliptic operators and the Mc Kean and Singer (Journal of Diff. Geometry, 1967) parametrix approach to the density expansion that has previously been extended to the degenerate setting that we consider (see Delarue and Menozzi, Journal of Funct. Analysis, 2010).
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https://hal.archives-ouvertes.fr/hal-00533300
Contributeur : Stephane Menozzi <>
Soumis le : lundi 8 novembre 2010 - 14:36:04
Dernière modification le : samedi 28 mars 2020 - 02:24:18
Document(s) archivé(s) le : mercredi 9 février 2011 - 02:43:31

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  • HAL Id : hal-00533300, version 1
  • ARXIV : 1011.1824

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Stephane Menozzi. Parametrix techniques and martingale problem for some degenerate Kolmogorov's equations. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2011, 16, pp.234-250. ⟨hal-00533300⟩

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