Abstract:
Advective skew dispersion is a natural Markov process defined ned
by a di ffusion with drift across an interface of jump discontinuity in
a piecewise constant diff usion coeffcient. In the absence of drift this
process may be represented as a function of -skew Brownian motion
for a uniquely determined value of = ; see Ramirez, Thomann,
Waymire, Haggerty and Wood (2006). In the present paper the analysis is extended to the case of non-zero drift. A determination of the (joint) distributions of key functionals of standard skew Brownian motion together with some associated probabilistic semigroup and local time theory is given for these purposes. An application to
the dispersion of a solute concentration across an interface is provided that explains certain symmetries and asymmetries in recently
reported laboratory experiments conducted at Lawrence-Livermore
Berkeley Labs by Berkowitz, Cortis, Dror and Scher (2009).
