Useful martingales for stochastic storage processes with L\'evy-type input and decomposition results

By Offer Kella, O. Boxma. 2011

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A Martingale Review of some Fluctuation Theory for Spectrally Negative Lévy Processes (2005, background): “A martingale which plays a fundamental role in our calculations is what we shall call the Kella-Whitt martingale, introduced in Kella and Whitt (1992).”
Matrix‐analytic Models and their Analysis (2000, background): “The reader interested in further martingale ideas is encouraged to study Kella & Whitt (1992) who gave some very useful martingales for re¯ected LeÂvy processes (Markov-modulated extensions appear in Asmussen & Kella, 2000).”
Fluctuations of spectrally negative Markov additive processes (2008, unknown): “This martingale is closely related to other martingales of an exponential type found in Kella and Whitt (1992) and Jacod and Shiryaev (1987) for example.”