| Título: | A set-indexed Ornstein-Uhlenbeck process |
| Autores: |
Balança, Paul; École Centrale Paris Herbin, Erick; École Centrale Paris |
| Fecha: | 2012-01-02 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Ornstein-Uhlenbeck process; Markov property; multiparameter and set-indexed processes; stationarity 60G10; 60G15; 60G60; 60J25 |
| Descripción: | 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. |
| Idioma: | Inglés |
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