%0 Journal Article %T A set-indexed Ornstein-Uhlenbeck process %A Paul Balan£¿a %A Erick Herbin %J Mathematics %D 2012 %I arXiv %R 10.1214/ECP.v17-1903 %X The purpose of this article is a set-indexed extension of the well-known Ornstein-Uhlenbeck process. The first part is devoted to a stationary definition of the random field and ends up with the proof of a complete characterization by its $L^2$-continuity, stationarity and set-indexed Markov properties. This specific Markov transition system allows to define a general \emph{set-indexed Ornstein-Uhlenbeck (SIOU) process} with any initial probability measure. Finally, in the multiparameter case, the SIOU process is proved to admit a natural integral representation. %U http://arxiv.org/abs/1203.5524v2