Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

4-1993

Publication Source

Proceedings of the American Mathematical Society

Volume

117

Issue

4

Start Page

1165

Last Page

1173

DOI

10.1090/S0002-9939-1993-1169048-2

Abstract

Features related to the perimeter of the convex hull C„ of a random walk in R2 are studied, with particular attention given to its length L„. Bounds on the variance of Ln are obtained to show that, for walks with drift, L„ obeys a strong law. Exponential bounds on the tail probabilities of L„ under special conditions are also obtained. We then develop simple expressions for the expected values of other features of Cn, including the number of faces, the sum of the lengths and squared lengths of the faces, and the number of faces of length t or less.

Copyright/Permission Statement

© Copyright 1993 American Mathematical Society

Keywords

Strong laws, convex hulls, random walks, Efron-Stein Inequality, variance bounds, geometric probability

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Mathematics Commons

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Date Posted: 27 November 2017

This document has been peer reviewed.