How long is the convex minorant of a one-dimensional random walk?

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
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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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