Electronic Communications in Probability

Parametrix techniques and martingale problems for some degenerate Kolmogorov equations

Stephane Menozzi

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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 [BP09] to prove uniqueness of the martingale problem in the framework of non- degenerate elliptic operators and the Mc Kean and Singer [MS67] parametrix approach to the density expansion that has previously been extended to the degenerate setting that we consider (see Delarue and Menozzi [DM10]).

Article information

Electron. Commun. Probab., Volume 16 (2011), paper no. 23, 234-250.

Accepted: 2 May 2011
First available in Project Euclid: 7 June 2016

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60G46: Martingales and classical analysis 60H30: Applications of stochastic analysis (to PDE, etc.)

Parametrix techniques Martingale problem hypoelliptic equations

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Menozzi, Stephane. Parametrix techniques and martingale problems for some degenerate Kolmogorov equations. Electron. Commun. Probab. 16 (2011), paper no. 23, 234--250. doi:10.1214/ECP.v16-1619. https://projecteuclid.org/euclid.ecp/1465261979

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