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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Comparing the distribution of various suprema on two-parameter Wiener space


Authors: Ian Pierce and David Skoug
Journal: Proc. Amer. Math. Soc. 141 (2013), 2149-2152
MSC (2010): Primary 60G15, 60G17, 60G40
Published electronically: February 12, 2013
MathSciNet review: 3034441
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Abstract: Let $ Q=[0,S]\times [0,T]$ and let $ C_2(Q)$ be two-parameter Wiener space. In this note we consider the ratios of the probabilities $ \mathbb{P}[x(S,T)\geq c]$, $ \mathbb{P}[\sup _{Q} x(s,t)\geq c]$ and $ \mathbb{P}[\sup _{\partial Q} x(s,t)\geq c]$.


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Additional Information

Ian Pierce
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
Address at time of publication: Department of Mathematics, Statistics & Computer Science, St. Olaf College, Northfield, Minnesota 55057
Email: s-ipierce1@math.unl.edu, pierce@stolaf.edu

David Skoug
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
Email: dskoug1@math.unl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11497-8
Keywords: Yeh-Wiener process, Brownian sheet, distribution of supremum
Received by editor(s): January 13, 2011
Received by editor(s) in revised form: October 7, 2011
Published electronically: February 12, 2013
Additional Notes: The authors wish to acknowledge the recommendations of an anonymous referee, whose advice helped to significantly shorten and clarify the arguments presented here.
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.