Levy-driven causal CARMA random fields

[摘要] We introduce Levy-driven causal CARMA random fields on R-d, extending the class of CARMA processes. The definition is based on a system of stochastic partial differential equations which generalize the classical state-space representation of CARMA processes. The resulting CARMA model differs fundamentally from the CARMA random field of Brockwell and Matsuda. We show existence of the model under mild assumptions and examine some of its features including the second-order structure and path properties. In particular, we investigate the sampling behavior and formulate conditions for the causal CARMA random field to be an ARMA random field when sampled on an equidistant lattice. (C) 2020 Elsevier B.V. All rights reserved.

[发布日期] 2020-12-01

[关键词] CARMA random field;Levy basis;Mild solution;Path property;Space-time modeling;SPDE