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A set-indexed Ornstein-Uhlenbeck process

   
@article{ECP1903,
	author = {Paul Balança and Erick Herbin},
	title = {A set-indexed Ornstein-Uhlenbeck process},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {17},
	year = {2012},
	keywords = {Ornstein-Uhlenbeck process; Markov property; multiparameter and set-indexed processes; stationarity},
	abstract = {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 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.},
	pages = {no. 39, 1-14},
	issn = {1083-589X},
	doi = {10.1214/ECP.v17-1903},    
        url = {http://ecp.ejpecp.org/article/view/1903}}