Abstract
Let Z(n) be the n-parameters Ornstein-Uhlenbeck process on a separable Fréchet gaussian space (E,μ). We consider the Sobolev space Wn,2 and the associated Gaussian capacity c n,2. We prove two inequalities of the following type:
These inequalities are used to give probabilistic representations for measures which belong to the dual space of Wn,2 and such representations permit us to prove that a Borel subset B of E has null cn,2-capacity if and only if Z(n) can not hit it.
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Song, S. (1993). Inegalites relatives aux processus d'Ornnstein-Uhlenbeck a n-parametres et capacite gaussienne cn,2 . In: Séminaire de Probabilités XXVII. Lecture Notes in Mathematics, vol 1557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087981
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DOI: https://doi.org/10.1007/BFb0087981
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