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Coupling iterated Kolmogorov diffusions
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Kendall, W. S. and Price, Catherine J. (2004) Coupling iterated Kolmogorov diffusions. Electronic Journal of Probability, Vol.9 (No.13). pp. 382-410. ISSN 1083-6489.
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Abstract
The Kolmogorov (1934) diffusion is the two-dimensional diffusion generated by real Brownian motion B and its time integral integral B d t. In this paper we construct successful co-adapted couplings for iterated Kolmogorov diffusions defined by adding iterated time integrals integral integral B d s d t,... as further components to the original Kolmogorov diffusion. A Laplace-transform argument shows it is not possible successfully to couple all iterated time integrals at once; however we give an explicit construction of a successful co-adapted coupling method for (B, integral B d t, integral integral B d s d t); and a more implicit construction of a successful co-adapted coupling method which works for finite sets of iterated time integrals.
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): | Diffusion processes, Brownian motion processes | ||||
Journal or Publication Title: | Electronic Journal of Probability | ||||
Publisher: | University of Washington. Dept. of Mathematics | ||||
ISSN: | 1083-6489 | ||||
Official Date: | 2004 | ||||
Dates: |
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Volume: | Vol.9 | ||||
Number: | No.13 | ||||
Number of Pages: | 29 | ||||
Page Range: | pp. 382-410 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 4 December 2015 | ||||
Date of first compliant Open Access: | 4 December 2015 |
Data sourced from Thomson Reuters' Web of Knowledge
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