Alsmeyer, Gerold, Kabluchko, Zakhar, Marynych, Alexander V and Vysotsky, Vladislav (2020) How long is the convex minorant of a one-dimensional random walk? Electronic Journal of Probability, 25 (a105). pp. 1-22. ISSN 1083-6489

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Abstract

We prove distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk with independent identically distributed increments. Depending on the increment law, there are several regimes with different limit distributions for this length. Among other tools, a representation of the convex minorant of a random walk in terms of uniform random permutations is utilized.

Item Type:	Article
Schools and Departments:	School of Mathematical and Physical Sciences > Mathematics
Related URLs:	https://projecteuclid.org/euclid.ejp/159...
SWORD Depositor:	Mx Elements Account
Depositing User:	Mx Elements Account
Date Deposited:	07 Aug 2020 09:58
Last Modified:	07 Sep 2020 14:00
URI:	http://sro.sussex.ac.uk/id/eprint/92972

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