| Issue |
ESAIM: PS
Volume 19, 2015
|
|
|---|---|---|
| Page(s) | 100 - 114 | |
| DOI | https://doi.org/10.1051/ps/2014016 | |
| Published online | 17 June 2015 | |
Operator scaled Wiener bridges∗
1
Faculty of Informatics, University of Debrecen,
Pf. 12, 4010
Debrecen,
Hungary
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2
Mathematisches Institut, Heinrich-Heine-Universität
Düsseldorf, Universitätsstr.
1, 40225
Düsseldorf,
Germany
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3
Keltenstr. 19, 41462
Neuss,
Germany
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Received:
28
August
2013
Abstract
We introduce operator scaled Wiener bridges by incorporating a matrix scaling in the drift part of the SDE of a multidimensional Wiener bridge. A sufficient condition for the bridge property of the SDE solution is derived in terms of the eigenvalues of the scaling matrix. We analyze the asymptotic behavior of the bridges and briefly discuss the question whether the scaling matrix determines uniquely the law of the corresponding bridge.
Mathematics Subject Classification: 60G15 / 60F15 / 60G17 / 60J60
Key words: Multidimensional Wiener bridge / operator scaling / strong law of large numbers / asymptotic behavior
The research of M. Barczy was realized in the frames of TÁMOP 4.2.4. A/2-11-1-2012-0001, National Excellence Program – Elaborating and operating an inland student and researcher personal support system”. The project was subsidized by the European Union and co-financed by the European Social Fund.
© EDP Sciences, SMAI, 2015
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