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What is Learnable in Valiant's Theory of the Learnable? 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High frequency sampling of a continuous-time ARMA process
Peter J. Brockwell, Vincenzo Ferrazzano, Claudia Klüppelberg · 2011-04-04 · via math.ST updates on arXiv.org

Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{nΔ}, n=0,1,2,...$, where $Δ$ is small and positive. Such data occur in many fields of application, particularly in finance and the study of turbulence. This paper is concerned with the characteristics of the process $(Y_{nΔ})_{n\in\bbz}$, when $Δ$ is small and the underlying continuous-time process $(Y_t)_{t\in\bbr}$ is a specified CARMA process.

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