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.
Regularization of differential equations by fractional noise
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Zero-noise limit of singular ODE regularized by fractional noise converges to extremal solutions with subexponential probability estimates.
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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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Zero noise limit for singular ODE regularized by fractional noise
Zero-noise limit of singular ODE regularized by fractional noise converges to extremal solutions with subexponential probability estimates.