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Recurrence and transience of reflecting Brownian motion in the quadrant

Published online by Cambridge University Press:  24 October 2008

D. G. Hobson  and
L. C. G. ROGERS
D. G. Hobson
Affiliation:
Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB
L. C. G. ROGERS
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London, E1 4NS
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Extract

In this paper we obtain criteria for a reflecting Brownian motion in the first orthant of the plane to reach an arbitrary open neighbourhood of the origin in finite time, or in finite mean time. The reflecting Brownian motion (RBM) is assumed to have a constant non-zero drift, and a constant non-singular covariance, and the directions of reflection on the two sides of are constant along each side, but not necessarily normal. We explain why the criteria we find are to be expected.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 2 , March 1993 , pp. 387 - 399
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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