Diffusions with reflection on an orthant and associated initial-boundary value problems
type: Item
instance of: scholarly article
title: Diffusions with reflection on an orthant and associated initial-boundary value problems
zbMATH Open document ID: 0533.60088
DOI: 10.1016/S0196-8858(82)80014-6
author: Ioannis Karatzas
published in: Advances in Applied Mathematics
publication date: 1982-01-01T00:00:00Z
review text: The abstract of the paper is adequate and I quote ''A class of diffusion processes with instantaneous reflection on the hyperplanes of an orthant is considered. In the case of constant drift and covariance coefficients, such diffusions arise as limits of properly normalized queue length processes in open queueing networks, under heavy traffic conditions. The directions of the reflection on each hyperplane determine the boundary data in an associated initial-boundary value problem with oblique derivatives for the corresponding Kolmogorov equation. This problem is studied in terms of single layer potentials with densities placed on the hyperplanes of the orthant, and is shown to be equivalent to solving a system of integral equations for those densities. The stochastic representation of the solution is also derived.''
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60K20
zbMATH DE Number: 3846617
zbMATH Keywords: reflection on hyperplanes
zbMATH Keywords: open queueing networks
zbMATH Keywords: heavy traffic conditions
reviewed by: G. Ananthakrishna
MaRDI profile type: Publication
cites work: Q5612227
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description: scientific article; zbMATH DE number 3846617