= Solution
For an SDE driven by Brownian motion, a <strong solution of a stochastic differential equation> is adapted to the completed filtration generated by a prescribed Brownian motion and satisfies the equation on that space. A <weak solution of a stochastic differential equation> consists of a probability space, filtration, Brownian motion, and adapted solution satisfying the equation. <Uniqueness in law> means that any two weak solutions with the same initial law have the same law as processes. <Pathwise uniqueness> means that two solutions on the same filtered space, driven by the same Brownian motion and having the same initial value, are indistinguishable.
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