How long is the convex minorant of a one-dimensional random walk?
| Autor: | Zakhar Kabluchko, Gerold Alsmeyer, Alexander Marynych, Vladislav Vysotsky |
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| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Discrete mathematics Independent identically distributed 60F05 60G55 (Primary) 60J10 (Secondary) Probability (math.PR) random permutation Regular polygon Random permutation convex minorant Random walk random walk 60F05 FOS: Mathematics 60J10 60G55 Limit (mathematics) Statistics Probability and Uncertainty Representation (mathematics) Mathematics - Probability Mathematics |
| Zdroj: | Electron. J. Probab. |
| ISSN: | 1083-6489 |
| Popis: | 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. 21 pages, 1 figure, to appear in the Electronic Journal of Probability |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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