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2020 $\varepsilon $-strong simulation of the convex minorants of stable processes and meanders
Jorge I. González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
Electron. J. Probab. 25: 1-33 (2020). DOI: 10.1214/20-EJP503

Abstract

Using marked Dirichlet processes we characterise the law of the convex minorant of the meander for a certain class of Lévy processes, which includes subordinated stable and symmetric Lévy processes. We apply this characterisation to construct $\varepsilon $-strong simulation ($\varepsilon $SS) algorithms for the convex minorant of stable meanders, the finite dimensional distributions of stable meanders and the convex minorants of weakly stable processes. We prove that the running times of our $\varepsilon $SS algorithms have finite exponential moments. We implement the algorithms in Julia 1.0 (available on GitHub) and present numerical examples supporting our convergence results.

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Jorge I. González Cázares. Aleksandar Mijatović. Gerónimo Uribe Bravo. "$\varepsilon $-strong simulation of the convex minorants of stable processes and meanders." Electron. J. Probab. 25 1 - 33, 2020. https://doi.org/10.1214/20-EJP503

Information

Received: 27 November 2019; Accepted: 26 July 2020; Published: 2020
First available in Project Euclid: 13 August 2020

zbMATH: 07252728
MathSciNet: MR4136476
Digital Object Identifier: 10.1214/20-EJP503

Subjects:
Primary: 60G17, 60G51, 65C05, 65C50

JOURNAL ARTICLE
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