 On a multidimensional Brownian motion with a membrane located on a given hyperplaneB.I. Kopytko and M.I. Portenko Stochastic Processes and their Applications, 2023, vol. 160, issue C, 371-385 Abstract: Brownian motion in a Euclidean space with a membrane located on a hyperplane and acting in the normal direction is constructed such that its so-called permeability coefficient can be given by an arbitrary Borel measurable function defined on that hyperplane and taking on its values from the interval [−1,1]. In all the publications on the topic, that coefficient was supposed to be a continuous function. A certain limit theorem for the number of crossings through the membrane by the consecutive values of the process constructed at the instants of time 0, 1/n, 2/n, …, [nt]/n (for fixed t>0) is proved under the assumption that n→∞. The limit distribution in that theorem can be curiously interpreted in the case of a membrane whose permeability coefficient coincides with the indicator of a measurable subset of the hyperplane. Keywords: Brownian motion; Partly permeable membrane; Single layer potential; Feynman–Kac formula; Local time (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:160:y:2023:i:c:p:371-385 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2023.03.011 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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