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Occupation and local times for skew Brownian motion with applications to dispersion across an interface

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  • 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).
  • Keywords: stochastic order, occupation time, Skew Brownian motion, local time, first passage time, advection-diffusion, elastic skew Brownian motion
  • Keywords: stochastic order, occupation time, Skew Brownian motion, local time, first passage time, advection-diffusion, elastic skew Brownian motion
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  • T. A. Appuhamillage, V. A. Bokil, E. Thomann, E. Waymire and B. Wood, Occupation and Local Times for Skew Brownian Motion with Applications to Dispersion Across an Interface, Annals of Applied Probability, accepted, to appear, 2010
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  • This research was partially supported by the grant Grant CMG EAR-0724865 from the National Science Foundation.
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