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...
Nearly fifty years after the introduction of skew Brownian motion by Itô and
McKean (1963), the first passage time distribution remains unknown. In this
paper, we first generalize results of Pitman and Yor (2001) and Csáki and Hu
(2004) to derive formulae for the distribution of ranked excursion heights of...
Results are provided that highlight the effect of interfacial discontinuities in the
diffusion coefficient on the behavior of certain basic functionals of the diffusion, such
as local times and occupation times, extending previous results in [2, 3] on the behavior
of first passage times. The main goal is to obtain...
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with formulations in terms of partial differential equations governing the conservative, advective-dispersive transport of mass concentrations in divergence form,...