It is shown that in the sense of Baire category, almost all stochastic differential equations with uniformly bounded measurable coefficients and uniformly nondegenerate diffusions have unique strong solutions.
"On the Prevalence of Stochastic Differential Equations with Unique Strong Solutions." Ann. Probab. 14 (2) 653 - 662, April, 1986. https://doi.org/10.1214/aop/1176992535