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Coupling the Kolmogorov diffusion : maximality and efficiency considerations
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Banerjee, Sayan and Kendall, W. S. (2016) Coupling the Kolmogorov diffusion : maximality and efficiency considerations. Advances in Applied Probability, 48 (A). pp. 15-35. doi:10.1017/apr.2016.40 ISSN 0001-8678.
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Official URL: http://dx.doi.org/10.1017/apr.2016.40
Abstract
This is a case study concerning the rate at which probabilistic coupling occurs for nilpotent diffusions. We focus on the simplest case of Kolmogorov diffusion (Brownian motion together with its time integral, or, slightly more generally, together with a finite number of iterated time integrals). In this case there can be no Markovian maximal coupling. Indeed, Markovian couplings cannot even be efficient (extending the terminology of Burdzy and Kendall, Efficient Markovian couplings: examples and counterexamples; Annals of Applied Probability, 2000). Finally, at least in the classical case of a single time integral, it is not possible to choose a Markovian coupling that is optimal in the sense of simultaneously minimizing the probability of failing to couple by time t for all positive t. In recompense for all these negative results, we exhibit a simple efficient non-Markovian coupling.
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): | Brownian motion processes | ||||||
Journal or Publication Title: | Advances in Applied Probability | ||||||
Publisher: | Applied Probability Trust | ||||||
ISSN: | 0001-8678 | ||||||
Official Date: | 25 July 2016 | ||||||
Dates: |
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Volume: | 48 | ||||||
Number: | A | ||||||
Page Range: | pp. 15-35 | ||||||
DOI: | 10.1017/apr.2016.40 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 22 May 2018 | ||||||
Date of first compliant Open Access: | 22 May 2018 | ||||||
RIOXX Funder/Project Grant: |
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