Spectral Representation of Gaussian Semimartingales

Andreas Basse ()
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Andreas Basse: University of Aarhus

Journal of Theoretical Probability, 2009, vol. 22, issue 4, 811-826

Abstract: Abstract The aim of the present paper is to characterize the spectral representation of Gaussian semimartingales. That is, we provide necessary and sufficient conditions on the kernel K for X t =∫ K t (s) dN s to be a semimartingale. Here, N denotes an independently scattered Gaussian random measure on a general space S. We study the semimartingale property of X in three different filtrations. First, the ℱ X -semimartingale property is considered, and afterwards the ℱ X,∞-semimartingale property is treated in the case where X is a moving average process and ℱ t X,∞ =σ(X s :s∈(−∞,t]). Finally, we study a generalization of Gaussian Volterra processes. In particular, we provide necessary and sufficient conditions on K for the Gaussian Volterra process ∫ −∞ t K t (s) dW s to be an ℱ W,∞-semimartingale (W denotes a Wiener process). Hereby we generalize a result of Knight (Foundations of the Prediction Process, 1992) to the nonstationary case.

Keywords: Semimartingales; Gaussian processes; Volterra processes; Stationary processes; Moving average processes; 60G15; 60G10; 60G48; 60G57 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-009-0246-2

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