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Representation of \(n\)-parameter Ornstein-Uhlenbeck processes. (Représentation du processus d’Ornstein-Uhlenbeck à \(n\) paramètres.) (French) Zbl 0798.60055

Azéma, J. (ed.) et al., Séminaire de probabilités XXVII. Berlin: Springer-Verlag. Lect. Notes Math. 1557, 302-303 (1993).
Let \(\{W(t_ 1, \dots, t_{n+1})\), \(t_ i \geq 0\}\) be an \((n+1)\)- parameter Wiener process. The author shows that the \(n\)-parameter \(C_ 0 (\mathbb{R}_ +)\)-valued process \[ Z(t_ 1, \dots, t_ n) = e^{-(t_ 1 + \cdots + t_ n)} W(e^{2t_ 1}, \dots, e^{2t_ n}, \cdot) \] coincides with the \(n\)-parameter Ornstein-Uhlenbeck process introduced by Song by using the iteration of the Ornstein-Uhlenbeck semigroup.
For the entire collection see [Zbl 0780.00013].

MSC:

60G60 Random fields
60J60 Diffusion processes
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