@article{EJP201,
author = {Wilfrid Kendall and Catherine Price},
title = {Coupling Iterated Kolmogorov Diffusions},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {9},
year = {2004},
keywords = {},
abstract = {The Kolmogorov-1934 diffusion is the two-dimensional diffusion generated by real Brownian motion and its time integral. In this paper we construct successful co-adapted couplings for iterated Kolmogorov diffusions defined by adding iterated time integrals 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 Brownian motion, its time integral, and its twice-iterated time integral; and a more implicit construction of a successful co-adapted coupling method which works for finite sets of iterated time integrals.},
pages = {no. 13, 382-410},
issn = {1083-6489},
doi = {10.1214/EJP.v9-201},
url = {http://ejp.ejpecp.org/article/view/201}}