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Optimal Markovian coupling for finite activity Lévy processes
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Kendall, W. S., Majka, Mateusz B. and Mijatović, Aleksandar (2023) Optimal Markovian coupling for finite activity Lévy processes. Bernoulli Journal . ISSN 1350-7265. (In Press)
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Official URL: https://www.bernoullisociety.org/index.php/publica...
Abstract
We study optimal Markovian couplings of Markov processes, where the optimality is understood in terms of minimization of concave transport costs between evaluations of the coupled processes at corresponding times.
We provide explicit constructions of such optimal couplings for one-dimensional finite-activity Lévy processes (continuous-time random walks) whose jump distributions are unimodal but not necessarily symmetric. Remarkably, the optimal Markovian coupling does not depend on the specific concave transport cost. To this end, we combine McCann’s results on optimal transport and Rogers’ results on random walks with a novel uniformization construction that allows us to characterize all Markovian couplings of finite-activity Lévy processes. In particular,
we show that the optimal Markovian coupling for finite-activity Lévy processes with non-symmetric unimodal Lévy measures has to allow for non-simultaneous jumps of the two coupled processes.
Item Type: | Journal Article | |||||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Markov processes, Lévy processes, Random walks (Mathematics) | |||||||||||||||||||||
Journal or Publication Title: | Bernoulli Journal | |||||||||||||||||||||
Publisher: | Int. Statistical Institute | |||||||||||||||||||||
ISSN: | 1350-7265 | |||||||||||||||||||||
Official Date: | 2023 | |||||||||||||||||||||
Dates: |
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Status: | Peer Reviewed | |||||||||||||||||||||
Publication Status: | In Press | |||||||||||||||||||||
Access rights to Published version: | Free Access (unspecified licence, 'bronze OA') | |||||||||||||||||||||
Date of first compliant deposit: | 31 October 2023 | |||||||||||||||||||||
Date of first compliant Open Access: | 31 October 2023 | |||||||||||||||||||||
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