Electronic Communications in Probability

Parametrix techniques and martingale problems for some degenerate Kolmogorov equations

Stephane Menozzi

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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 [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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465261979

Digital Object Identifier
doi:10.1214/ECP.v16-1619

Mathematical Reviews number (MathSciNet)
MR2802040

Zentralblatt MATH identifier
1225.60097

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

Keywords
Parametrix techniques Martingale problem hypoelliptic equations

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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References

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