Abstract
For a stochastic differential equation of the form with B a Brownian motion, uniqueness in law can be defined in two different ways: the usual one (for all solutions the law of is the same), and a stronger one (all solutions have the same law). These two definitions are shown to be equivalent; more precisely, when the law of is extremal in the set of all laws of solutions, the law of is determined by that of.
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© 2003 Springer-Verlag Berlin Heidelberg
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Brossard, J. (2003). Deux notions équivalentes d’unicité en loi pour les équations différentielles stochastiques. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVII. Lecture Notes in Mathematics, vol 1832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40004-2_10
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DOI: https://doi.org/10.1007/978-3-540-40004-2_10
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Publisher Name: Springer, Berlin, Heidelberg
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