On the Uniqueness in Law and the Pathwise Uniqueness for Stochastic Differential Equations

By Alexander S. Cherny, PII. S0040585X97979093. 2002

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Stochastic differential equations for sticky Brownian motion (2014, background): “151–155]) and the left-arrow implication was established by a number of authors (see Engelbert [6] and the references therein) including Cherny [2] who showed H.”
The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities (2007, background): “For Itô equations, however, Cherny (6) has shown that it is sufficient to assume uniqueness in distribution for the solution X.”
Strong solutions of stochastic equations with rank-based coefficients (2011, unknown): “1 in [5] shows that the joint laws of the triples (τ,X([0, τ ]),W ([0, τ ])) and (τ̂ , X̂([0, τ̂ ]),W ([0, τ̂ ])) are the same.”