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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.

OriginalsprogEngelsk
TidsskriftStochastic Processes and Their Applications
Vol/bind129
Nummer10
Sider (fra-til)4119-4143
Antal sider25
ISSN0304-4149
DOI
StatusUdgivet - 1 okt. 2019

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