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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. 382410. ISSN 10836489

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Abstract
The Kolmogorov (1934) diffusion is the twodimensional diffusion generated by real Brownian motion B and its time integral integral B d t. In this paper we construct successful coadapted 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 Laplacetransform argument shows it is not possible successfully to couple all iterated time integrals at once; however we give an explicit construction of a successful coadapted coupling method for (B, integral B d t, integral integral B d s d t); and a more implicit construction of a successful coadapted 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:  10836489 
Official Date:  2004 
Volume:  Vol.9 
Number:  No.13 
Number of Pages:  29 
Page Range:  pp. 382410 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Open Access 
References:  Aldous, D. J. and H. Thorisson (1993). Shiftcoupling. Stochastic Processes and Their 
URI:  http://wrap.warwick.ac.uk/id/eprint/8159 
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