Coupling Iterated Kolmogorov Diffusions
Wilfrid S Kendall, University of Warwick
Catherine J. Price, Lehman Brothers
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.
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