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We show weak existence and uniqueness in law for a general class of stochastic differential equations in Rᵈ, d 1, with prescribed sub-invariant measure. The dispersion and drift coefficients of the stochastic differential equation are allowed to be degenerate and discontinuous, and locally unbounded, respectively. Uniqueness in law is obtained via L¹ (Rᵈ, ) -uniqueness in a subclass of continuous Markov processes, namely right processes that have as sub-invariant measure and have continuous paths for -almost every starting point. Weak existence is obtained for a broader class via the martingale problem.
Lee et al. (Tue,) studied this question.