= Strong existence theorem for additive-noise SDEs with bounded measurable drift
= Veretennikov theorem for bounded drift and additive noise
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For bounded Borel $b:\mathbb R^d\to\mathbb R^d$, the <stochastic differential equation> $dX_t=b(X_t)dt+dB_t$ has <strong existence> and <pathwise uniqueness>. The identity diffusion matrix is nondegenerate. A <Girsanov theorem> argument alone establishes weak existence and <uniqueness in law>; the strong conclusion requires an additional theorem. This statement does not extend without further hypotheses to arbitrary path-dependent drift or arbitrary diffusion matrices. See https://www.mathnet.ru/php/archive.phtml?jrnid=sm&option_lang=eng&paperid=2601&wshow=paper[the primary bounded-drift strong-solution theorem].
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