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Lévy-driven causal CARMA random fields

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  • Pham, Viet Son

Abstract

We introduce Lévy-driven causal CARMA random fields on Rd, 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.

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  • Pham, Viet Son, 2020. "Lévy-driven causal CARMA random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7547-7574.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:12:p:7547-7574
    DOI: 10.1016/j.spa.2020.08.006
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    References listed on IDEAS

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