OCCUPATION AND LOCAL TIMES FOR SKEW BROWNIAN MOTION WITH APPLICATIONS TO DISPERSION ACROSS AN INTERFACE

• 成果类型: Article
• 署名作者: Appuhamillage, Thilanka; Bokil, Vrushali; Thomann, Enrique; Waymire, Edward; Wood, Brian
• 署名单位: Oregon State University; Oregon State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP691
• 发表日期: 2011
• 页码: 183-214
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; diffusion-processes; porous-media; discontinuous coefficients; transport

摘要

Advective skew dispersion is a natural Markov process defined by a diffusion with drift across an interface of jump discontinuity in a piecewise constant diffusion coefficient. In the absence of drift, this process may be represented as a function of alpha-skew Brownian motion for a uniquely determined value of alpha = alpha*; see Ramirez et al. [Multiscale Model. Simul. 5 (2006) 786-801]. In the present paper, the analysis is extended to the case of nonzero 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 et al. [Water Resour Res. 45 (2009) W02201].