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Open AccessArticle

Well-Posedness for a Class of Degenerate Itô Stochastic Differential Equations with Fully Discontinuous Coefficients

1
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
2
Department of Mathematical Sciences and Research Institute, Mathematics of Seoul National University, 1 Gwanak-Ro, Gwanak-Gu, Seoul 08826, Korea
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(4), 570; https://doi.org/10.3390/sym12040570
Received: 14 February 2020 / Revised: 9 March 2020 / Accepted: 12 March 2020 / Published: 5 April 2020
(This article belongs to the Special Issue Advances in Stochastic Differential Equations)
We show uniqueness in law for a general class of stochastic differential equations in R d , d 2 , with possibly degenerate and/or fully discontinuous locally bounded coefficients among all weak solutions that spend zero time at the points of degeneracy of the dispersion matrix. Points of degeneracy have a d-dimensional Lebesgue–Borel measure zero. Weak existence is obtained for a more general, but not necessarily locally bounded drift coefficient. View Full-Text
Keywords: degenerate stochastic differential equation; uniqueness in law; martingale problem; weak existence; strong Feller semigroup. degenerate stochastic differential equation; uniqueness in law; martingale problem; weak existence; strong Feller semigroup.
MDPI and ACS Style

Lee, H.; Trutnau, G. Well-Posedness for a Class of Degenerate Itô Stochastic Differential Equations with Fully Discontinuous Coefficients. Symmetry 2020, 12, 570.

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