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A Parametrix Approach for some Degenerate Stable Driven SDEs

Abstract : We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak Hörmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the associated generator under some dimension constraints. Also, when the driving noise is scalar and tempered, we establish density bounds reflecting the multi-scale behavior of the process.
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https://hal.archives-ouvertes.fr/hal-00947749
Contributor : Stephane Menozzi <>
Submitted on : Wednesday, March 4, 2015 - 4:06:36 PM
Last modification on : Saturday, March 28, 2020 - 2:11:49 AM
Document(s) archivé(s) le : Friday, June 5, 2015 - 11:06:58 AM

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  • HAL Id : hal-00947749, version 2
  • ARXIV : 1402.3997

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Lorick Huang, Stephane Menozzi. A Parametrix Approach for some Degenerate Stable Driven SDEs. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2016, 52 (4), pp.1925-1975. ⟨hal-00947749v2⟩

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