Markovian structure in the concave majorant of Brownian motion
| Autor: | Mehdi Ouaki, Jim Pitman |
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| Rok vydání: | 2021 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2105.11042 |
| Popis: | The purpose of this paper is to highlight some hidden Markovian structure of the concave majorant of the Brownian motion. Several distributional identities are implied by the joint law of a standard one-dimensional Brownian motion $B$ and its almost surely unique concave majorant $K$ on $[0,\infty)$. In particular, the one-dimensional distribution of $2 K_t - B_t$ is that of $R_5(t)$, where $R_5$ is a $5-$dimensional Bessel process with $R_5(0) = 0$. The process $2K-B$ shares a number of other properties with $R_5$, and we conjecture that it may have the distribution of $R_5$. We also describe the distribution of the convex minorant of a three-dimensional Bessel process with drift. Comment: 24 pages. To appear in Electron. J. Probab |
| Databáze: | OpenAIRE |
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