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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Jordan curves in the level sets of additive Brownian motion


Authors: Robert C. Dalang and T. Mountford
Journal: Trans. Amer. Math. Soc. 353 (2001), 3531-3545
MSC (2000): Primary 60G60; Secondary 60G15
Published electronically: April 24, 2001
MathSciNet review: 1837246
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Abstract:

This paper studies the topological and connectivity properties of the level sets of additive Brownian motion. More precisely, for each excursion set of this process from a fixed level, we give an explicit construction of a closed Jordan curve contained in the boundary of this excursion set, and in particular, in the level set of this process.


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Additional Information

Robert C. Dalang
Affiliation: Département de Mathématiques, Ecole Polytechnique Fédérale, 1015 Lausanne, Switzerland
Email: robert.dalang@epfl.ch

T. Mountford
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90024
Email: malloy@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02811-2
PII: S 0002-9947(01)02811-2
Keywords: Additive Brownian motion, Brownian sheet, level set, Jordan curve
Received by editor(s): May 11, 2000
Published electronically: April 24, 2001
Additional Notes: The research of the first author is partially supported by the Swiss National Foundation for Scientific Research
The research of the second author is partially supported by NSF grant DMS-9703815 and by the Sloan Foundation
Article copyright: © Copyright 2001 American Mathematical Society