We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathwise uniqueness does not hold nor does a strong solution exist.
"A stochastic differential equation with a sticky point." Electron. J. Probab. 19 1 - 22, 2014. https://doi.org/10.1214/EJP.v19-2350