%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