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

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 degenerac...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 12; no. 4; p. 570
Main Authors Lee, Haesung, Trutnau, Gerald
Format Journal Article
LanguageEnglish
Published MDPI AG 01.04.2020
Subjects
degenerate stochastic differential equation
martingale problem
strong Feller semigroup
uniqueness in law
weak existence
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym12040570