2000/04/20 by Toufic Suidan, Suidan, Toufic
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60C05 #60Gxx #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60C05 #msc:60Gxx
paper · pdf · doi:10.48550/arxiv.math/0004131
withdrawn
openalex publication_date 2000/04/20 · arxiv created 2003/11/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This 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.