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Convex minorants and the fluctuation theory of Lévy processes. LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS 2022. [DOI: 10.30757/alea.v19-39] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Cygan W, Sandrić N, Šebek S. Convex hulls of stable random walks. ELECTRON J PROBAB 2022. [DOI: 10.1214/22-ejp826] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Wojciech Cygan
- Technische Universität Dresden, Faculty of Mathematics, Institute of Mathematical Stochastics, Zellescher Weg 25, 01069 Dresden, Germany
| | - Nikola Sandrić
- Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
| | - Stjepan Šebek
- Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia
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Ouaki M, Pitman J. Markovian structure in the concave majorant of Brownian motion. ELECTRON J PROBAB 2022. [DOI: 10.1214/22-ejp769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Mehdi Ouaki
- Department of Statistics, 451 Evans Hall, University of California at Berkeley, Berkeley, USA
| | - Jim Pitman
- Department of Statistics, 367 Evans Hall, University of California at Berkeley, Berkeley, USA
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Abstract
AbstractWe exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpetuity equation for the supremum (via the representation of the concave majorants of Lévy processes [27]) and use it to construct a Markov chain in the DCFTP algorithm. We prove that the number of steps taken backwards in time before the coalescence is detected is finite. We analyse the performance of the algorithm numerically (the code, written in Julia 1.0, is available on GitHub).
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Groeneboom P, Jongbloed G. Some Developments in the Theory of Shape Constrained Inference. Stat Sci 2018. [DOI: 10.1214/18-sts657] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Lambert A, Uribe Bravo G. Totally ordered measured trees and splitting trees with infinite variation. ELECTRON J PROBAB 2018. [DOI: 10.1214/18-ejp251] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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