Lévy driven moving averages and semimartingales

By A. Basse, Jan Pedersen. 2009

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Brownian Semistationary Processes and Volatility/Intermittency (2009, unknown): “At a further level of generalisation, Basse and Pedersen, in Basse and Pedersen (2008), consider processesX of the general form Xt = ∫ t −∞ (φ (t− s) − ψ (−s)) dLs whereL is a (two-sided) nondeterministic Lévy process with characteristic triplet ( γ, σ2, ν ) , φ andψ are deterministic functions…”
A weak solution theory for stochastic Volterra equations of convolution type (2019, background): “The most basic ones are Lévy driven moving averages where the characteristics of the driving semimartingale are constant and thus do not depend on X (Basse and Pedersen, 2009; Marquardt, 2006).”
Modelling energy spot prices by volatility modulated Levy-driven Volterra processes (2013, background): “That is, throughout the rest of the paper, let Y t = ∫ t −∞ G(t, s)ωs− dLs, Yt = ∫ t −∞ g(t− s)ωs− dLs, t ∈R. (3) In this paper, we use the stochastic integration concept described in Basse-O’Connor, Graversen and Pedersen [20] where a stochastic integration theory on R, rather than on compact inter”