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Convex minorants of random walks and Lévy processes

   
@article{ECP1648,
	author = {Josh Abramson and Jim Pitman and Nathan Ross and Geronimo Uribe Bravo},
	title = {Convex minorants of random walks and Lévy processes},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {Random walks, Lévy processes, Brownian meander, Convex minorant, Uniform  stick-breaking, Fluctuation theory},
	abstract = {This article provides an overview of recent work on descriptions and properties of the Convex minorants of random walks and Lévy processes, which summarize and extend the literature on these subjects.  The results surveyed include point process descriptions of the convex minorant of random walks and Lévy processes on a fixed finite interval, up to an independent exponential time, and in the infinite horizon case. These descriptions follow from the invariance of these processes under an adequate path transformation. In the case of Brownian motion, we note how further special properties of this process, including time-inversion, imply a sequential description for the convex minorant of the Brownian meander.},
	pages = {no. 38, 423-434},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1648},    
        url = {http://ecp.ejpecp.org/article/view/1648}}