Concave majorant of stochastic processes and Burgers turbulence. Lachieze-Rey, R. r̆lhttp://arxiv.org/abs/0909.1088v2, 2009.
Paper abstract bibtex In this paper, we study the convex hull of the graph of a stochastic process, and more precisely its extremal points. The times where those extremal points are reached, called extremal times, form a negligible set for Lévy processes, their integrated processes, and It\^o processes. We examine more closely the case of a Lévy process with bounded variation. Its extremal superior points are almost surely countable, with accumulation only around the extremal values.
@misc{Lachieze-Rey:2009fk,
Abstract = {In this paper, we study the convex hull of the graph of a stochastic process, and more precisely its extremal points. The times where those extremal points are reached, called extremal times, form a negligible set for L\'evy processes, their integrated processes, and It\^o processes. We examine more closely the case of a L\'evy process with bounded variation. Its extremal superior points are almost surely countable, with accumulation only around the extremal values.},
Author = {Raphael Lachieze-Rey},
Date-Added = {2011-02-08 10:51:18 -0600},
Date-Modified = {2011-02-08 10:51:18 -0600},
Eprint = {ArXiv:0909.1088v2},
Howpublished = {\url{http://arxiv.org/abs/0909.1088v2}},
Title = {Concave majorant of stochastic processes and {B}urgers turbulence},
Url = {http://arxiv.org/abs/0909.1088v2},
Year = {2009},
Bdsk-Url-1 = {http://arxiv.org/abs/0909.1088v2}}
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