Reflected Brownian motion in a cone: Semimartingale property |
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Authors: | Youngmee Kwon |
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Institution: | (1) Department of Computer Science and Statistics, Hansung University, 389 2 ga Samsun-dong Sungbuk-gu, 136-792 Seoul, Korea |
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Abstract: | Summary In this paper, the object of study is reflected Brownian motion in a cone ind-dimensions (d3) with nonconstant oblique reflection on each radial line emanating from the vertex of the cone. The basic question considered here is When is this process a semimartingale?. Conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by Kwon, which is resolved in terms of a real parameter depending on the cone and the direction of reflection. It is shown that starting from any point of the cone, the process is a semimartingale if < 1, + 0 and not a semimartingale if < < 2.This research is supported by KOSEF grant 941-0100-011-1 |
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Keywords: | 60J60 60J65 60G44 60K25 |
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