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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Published in | Symmetry (Basel) Vol. 12; no. 4; p. 570 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
MDPI AG
01.04.2020
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 2073-8994 2073-8994 |
DOI: | 10.3390/sym12040570 |