## 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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