Well-posedness for a class of degenerate Itô-SDEs with fully discontinuous coefficients

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.

arXiv commentLong version with all details (correction of typos)

References in corpus (2)

• Inverse Problem for a Curved Quantum Guide
• Existence and regularity of infinitesimally invariant measures, transition functions and time homogeneous Itô-SDEs

Cited by in corpus (5)

• Analytic theory of Itô-stochastic differential equations with non-smooth coefficients
• Variability of paths and differential equations with $BV$-coefficients
• Pointwise well-posedness results for degenerate Itô-SDEs with locally bounded drifts
• On the pathwise uniqueness for a class of degenerate Itô-stochastic differential equations
• Existence and uniqueness of (infinitesimally) invariant measures for second order partial differential operators on Euclidean space