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Everything is in the title, I'm looking for an example of an SDE with a unique strong solution but with multiple weak solutions.

Best regards.

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I would say they always have multiple weak solutions, since an probability space on which you provide a strong solution is a weak solution. –  mike Jun 21 '12 at 22:11
    
@ mike : Ok I'll edit my question to be more precise. Regards –  TheBridge Jun 22 '12 at 9:12
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