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

Stephane Menozzi (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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).

Keywords: Parametrix techniques; martingale problem; hypoelliptic equations

Domains: Probability [math.PR]; Analysis of PDEs [math.AP]

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