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

Abstract

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.

Keywords

• degenerate stochastic differential equation
• uniqueness in law
• martingale problem
• weak existence
• strong Feller semigroup.