AbstractLetbbe a Borel measurable IRd‐ valued function, defined on some Borel subset of IRd. Consider thed‐dimensional SDEwith singular driftb. A local solution (up to σ) is a tuple (X, W, Q,σ) whereXis a stochastic process,Wis a Brownian motion under the probability measure Q, and σ is a strictly optional time (i.e., stopping time) such that the above equation is satisfied for allt<σ. Such a local solution was constructed by the author in an earlier paper under very mild conditions onb. In this paper we give criteria for the global existence of the solution, i. e., for Q(σ
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