Coupling iterated Kolmogorov diffusions
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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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|
|Number of Pages:||29|
|Page Range:||pp. 382-410|
|Access rights to Published version:||Open Access|
Aldous, D. J. and H. Thorisson (1993). Shift-coupling. Stochastic Processes and Their
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