Statistical Properties of Convex Minorants of Random Walks and Brownian Motions

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dc.creatorSuidan, Toufic
dc.date2000-04-20
dc.date2003-11-30
dc.date.accessioned2026-07-07T04:34:49Z
dc.date.available2026-07-07T04:34:49Z
dc.descriptionThis paper calculates several useful statistical properties of the convex minorant process generated by random walk processes. In particular, we calculate the statistics of the longest segment in the convex minorant of a random walk of a given length. In addition, we calculate the probability that the convex minorant of a random walk of length N is composed of exactly m segments; we give an exact formula for the expected number of segments in the convex minorant. We obsevere that some of this analysis can be meaningful for the case of Brownian motion on finite intervals; we can calculate exact formulas for the density of the length of the longest segment in the convex minorant of Brownian motion on finite intervals.
dc.descriptionwithdrawn
dc.identifierhttps://arxiv.org/abs/math/0004131
dc.identifierhttp://arxiv.org/abs/math/0004131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59053
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60Gxx; 60C05
dc.titleStatistical Properties of Convex Minorants of Random Walks and Brownian Motions
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