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How long is the convex minorant of a one-dimensional random walk?
journal contribution
posted on 2023-06-07, 07:43 authored by Gerold Alsmeyer, Zakhar Kabluchko, Alexander V Marynych, Vladislav VysotskiyVladislav VysotskiyWe 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.
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- Published
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- Published version
Journal
Electronic Journal of ProbabilityISSN
1083-6489Publisher
Institute of Mathematical StatisticsExternal DOI
Issue
a105Volume
25Page range
1-22Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2020-08-07First Open Access (FOA) Date
2020-09-07First Compliant Deposit (FCD) Date
2020-09-07Usage metrics
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