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Joint density of the stable process and its supremum : regularity and upper bounds
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González Cázares, Jorge Ignacio, Kohatsu-Higa, Arturo and Mijatović, Aleksandar (2023) Joint density of the stable process and its supremum : regularity and upper bounds. Bernoulli, 29 (4). pp. 3443-3469. doi:10.3150/23-bej1590 ISSN 1350-7265.
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Official URL: http://doi.org/10.3150/23-bej1590
Abstract
This article uses a combination of three ideas from simulation to establish a nearly optimal polynomial upper bound for the joint density of the stable process and its associated supremum at a fixed time on the entire support of the joint law. The representation of the concave majorant of the stable process and the Chambers-Mallows-Stuck representation for stable laws are used to define an approximation of the random vector of interest. An interpolation technique using multilevel Monte Carlo is applied to accelerate the approximation, allowing us to establish the infinite differentiability of the joint density as well as nearly optimal polynomial upper bounds for the joint mixed derivatives of any order.
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||||||||
SWORD Depositor: | Library Publications Router | |||||||||||||||
Library of Congress Subject Headings (LCSH): | Machine learning, Bayesian statistical decision theory, Mathematical optimization, Stochastic processes, Probabilities | |||||||||||||||
Journal or Publication Title: | Bernoulli | |||||||||||||||
Publisher: | Bernoulli Society for Mathematical Statistics and Probability | |||||||||||||||
ISSN: | 1350-7265 | |||||||||||||||
Official Date: | 1 November 2023 | |||||||||||||||
Dates: |
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Volume: | 29 | |||||||||||||||
Number: | 4 | |||||||||||||||
Page Range: | pp. 3443-3469 | |||||||||||||||
DOI: | 10.3150/23-bej1590 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Re-use Statement: | . | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Copyright Holders: | © 2023 ISI/BS | |||||||||||||||
Date of first compliant deposit: | 15 November 2023 | |||||||||||||||
Date of first compliant Open Access: | 15 November 2023 | |||||||||||||||
RIOXX Funder/Project Grant: |
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