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A stochastic differential equation with a unique (up to indistinguishability) but not strong solution. (English) Zbl 0954.60046
Azéma, Jacques (ed.) et al., Séminaire de probabilités XXXIII. Berlin: Springer. Lect. Notes Math. 1709, 315-326 (1999).
An example of a stochastic differential equation is given with uniqueness property, that is, for each initial value there is a unique solution living on some probability space. This equation has another solution living on a different probability space and does not have strong solutions. This illustrates the fact that pathwise uniqueness is really needed for existence of strong solutions.
For the entire collection see [Zbl 0924.00016].

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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