= Weak existence and uniqueness in law for an additive-noise SDE with bounded drift
{c}
If $b:\mathbb R\to\mathbb R$ is bounded and measurable, then on every finite time interval
$$
dX_t=b(X_t)dt+dW_t
$$
has a weak solution and <uniqueness in law>. Starting with <Wiener measure>, the <Novikov condition> and <Girsanov theorem> add the drift. Applying the inverse change of measure to any weak solution recovers Wiener measure and identifies its law by the same pathwise density.
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