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Multivariate stochastic delay differential equations and CAR representations of CARMA processes

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In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a CAR(∞) representation. Furthermore, we show how the CAR(∞) representation gives rise to a prediction formula for CARMA processes. To be used in the above mentioned results we develop a general theory for multivariate stochastic delay differential equations, which will be of independent interest, and which will have particular focus on existence, uniqueness and representations.

Original languageEnglish
JournalStochastic Processes and Their Applications
Pages (from-to)4119-4143
Number of pages25
Publication statusPublished - 1 Oct 2019

    Research areas

  • CARMA processes, FICARMA processes, Long memory, MCARMA processes, Multivariate Ornstein–Uhlenbeck processes, Multivariate stochastic delay differential equations, Noise recovery, Prediction

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