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Coupling iterated Kolmogorov diffusions

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Kendall, Wilfrid 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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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
Date:	2004
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
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URI:	http://wrap.warwick.ac.uk/id/eprint/8159