Brownian motion in a euclidean space with a membrane located on a given hyperplane
DOI:
https://doi.org/10.15407/dopovidi2022.01.003Keywords:
Brownian motion, partly permeable membrane, single layer potential, Feynman—Kac formula, local timeAbstract
For the Brownian motion in a Euclidean space, a membrane located on a given hyperplane and acting in the normal direction is constructed such that its so-called permeability coefficient can be given by an arbitrary measurable function defined on that hyperplane and taking on its values in the interval [–1, 1]. In all the previous investigations on the topic that coefficient was supposed to be a continuous function. A limit theorem for the number of crossings of the hyperplane by a discrete approximation of the process constructed is proved. A curious interpretation for the limit distribution in that theorem can be given in the case of the membrane being porous.
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