Well-posedness for a class of degenerate It\^o-SDEs with fully discontinuous coefficients

Haesung Lee; Gerald Trutnau

doi:10.3390/sym12040570

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arXiv · 1909.09430

Well-posedness for a class of degenerate It\^o-SDEs with fully discontinuous coefficients

Haesung Lee·Gerald Trutnau

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Abstract

We show uniqueness in law for a general class of stochastic differential equations in $\mathbb{R}^d$, $d\ge 2$, 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. The points of degeneracy have $d$-dimensional Lebesgue-Borel measure zero. Weak existence is obtained for more general, not necessarily locally bounded drift coefficient.

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BibTeX RIS

Haesung Lee, Gerald Trutnau. 2019-09-20. Well-posedness for a class of degenerate It\^o-SDEs with fully discontinuous coefficients. https://doi.org/10.3390/sym12040570

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