Stability and Attraction to Normality for Lévy Processes at Zero and at Infinity

By R. Doney, Ross Maller. 2002

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STOCHASTIC INTEGRALS WITH RESPECT TO L´ EVY PROCESSES AND INFINITELY DIVISIBLE DISTRIBUTIONS (2011, methodology): “The expression of this condition in terms of the generating triplet of {Xt} is given by Sato [45] and Doney and Maller [12].”
Generalised Ornstein-Uhlenbeck Processes and the Convergence of Levy Integrals (2005, background): “s; Doney and Maller [12] show that this is equivalent to ∫ ∞”
STABILITY OF THE OVERSHOOT FOR LÉVY PROCESSES (2002, background): “Our first result is similar, in content and proof, to Proposition 2 of Bertoin [(1996), page 76].”
Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes (2005, methodology): “(2.5) Stationarity of (Vt)t≥0 is characterised in the following theorem, where we use E(·) to denote the stochastic exponential (as e.g. in Protter [27], page 85).”