Convex hulls of random walks and their scaling limits
Wade, Andrew R. and Xu, Chang (2015) Convex hulls of random walks and their scaling limits. Stochastic Processes and their Applications, 125 (11). pp. 4300-4320. ISSN 0304-4149 (https://doi.org/10.1016/j.spa.2015.06.008)
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Abstract
For the perimeter length and the area of the convex hull of the first n steps of a planar random walk, we study n→∞ mean and variance asymptotics and establish non-Gaussian distributional limits. Our results apply to random walks with drift (for the area) and walks with no drift (for both area and perimeter length) under mild moments assumptions on the increments. These results complement and contrast with previous work which showed that the perimeter length in the case with drift satisfies a central limit theorem. We deduce these results from weak convergence statements for the convex hulls of random walks to scaling limits defined in terms of convex hulls of certain Brownian motions. We give bounds that confirm that the limiting variances in our results are non-zero.
ORCID iDs
Wade, Andrew R. and Xu, Chang ORCID: https://orcid.org/0000-0003-2674-0034;-
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Item type: Article ID code: 54115 Dates: DateEventNovember 2015Published9 July 2015Published Online29 June 2015AcceptedSubjects: Science > Mathematics Department: University of Strathclyde > University of Strathclyde
Faculty of Science > Mathematics and StatisticsDepositing user: Pure Administrator Date deposited: 31 Aug 2015 10:17 Last modified: 27 Nov 2024 03:30 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/54115