For any α<0 there exist drifts u in L^∞_t C^α_x such that the additive SDE dX=u(t,X)dt+dB has unique weak solutions but fails pathwise uniqueness.
Path-by-path uniqueness for stochastic differential equations under Krylov - Röckner condition, July 2025
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Extends prior work with non-explosion criteria for bRDEs with unbounded coefficients, sharpness via pure-area path constructions, and a faster-growth variant.
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Sharp pathwise nonuniqueness for additive SDEs
For any α<0 there exist drifts u in L^∞_t C^α_x such that the additive SDE dX=u(t,X)dt+dB has unique weak solutions but fails pathwise uniqueness.
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Non-explosion principles for branched rough differential equations with unbounded coefficients
Extends prior work with non-explosion criteria for bRDEs with unbounded coefficients, sharpness via pure-area path constructions, and a faster-growth variant.