Martingale problems for some degenerate Kolmogorov equations
نویسندگان
چکیده
منابع مشابه
Martingale problems for some degenerate Kolmogorov equations
We obtain Calderón-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous nonlinear coefficients. We then derive the well-posedness of the martingale problem associated with related degenerate operators, and therefore uniqueness in law for the corresponding stochastic differential equations. Some density estimates are established as well.
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Equivalence of stochastic equations and martingale problems
The fact that the solution of a martingale problem for a diffusion process gives a weak solution of the corresponding Itô equation is well-known since the original work of Stroock and Varadhan. The result is typically proved by constructing the driving Brownian motion from the solution of the martingale problem and perhaps an auxiliary Brownian motion. This constructive approach is much more ch...
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We adapt the Levi’s parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2018
ISSN: 0304-4149
DOI: 10.1016/j.spa.2017.06.001