Some Martingales Associated to Reflected Lévy Processes

By L. Nguyen-Ngoc, Marc Yor. 2005

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An Excursion-Theoretical Approach to Some Boundary Crossing Problems and the Skorokhod Embedding for Reflected Lévy Processes (2007, methodology): “Kennedy’s analysis was extended to the case of diffusions by Azéma and Yor [3] and more recently a martingale proof was given by Nguyen and Yor [14] for the form of the Laplace transform of this stopping time in the case of spectrally negative Lévy processes.”
On Gerber–Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function (2011, background): “Details are omitted since these follow straightforwardly from [31], Proposition 1.”
Occupation densities in solving exit problems for Markov additive processes and their reflections (2011, methodology): “For Lévy processes this technique complements the use of martingales (see [29, 32, 6]), potential densities (see [36]), and excursion calculations (see [18, 35]).”
On the drawdown of completely asymmetric Lévy processes (2011, methodology): “[9,26], which rests on the identification of certain martingales, and the excursion-theoretic approach, employed in a.”
Doob's maximal identity, multiplicative decompositions and enlargements of filtrations (2005, background): “In [15], a special case of Proposition 2.”