Continuous-Time Autoregressive Moving-Average Processes in Hilbert Space

摘要

We introduce the class of continuous-time autoregressive moving-average(CARMA) processes in Hilbert spaces. As driving noises of these processes weconsider Levy processes in Hilbert space. We provide the basic definitions,show relevant properties of these processes and establish the equivalents ofCARMA processes on the real line. Finally, CARMA processes in Hilbert space arelinked to the stochastic wave equation and functional autoregressive processes.