Geodesic
Operator scaled Wiener bridges
Barczy, Mátyás1 ; Kern, Peter2 ; Krause, Vincent3
1 Faculty of Informatics, University of Debrecen, Pf. 12, 4010 Debrecen, Hungary
2 Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
3 Keltenstr. 19, 41462 Neuss, Germany
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 100-114

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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.

Reçu le :
DOI : 10.1051/ps/2014016
Classification : 60G15, 60F15, 60G17, 60J60
Keywords: Multidimensional Wiener bridge, operator scaling, strong law of large numbers, asymptotic behavior

Barczy, Mátyás 1 ; Kern, Peter 2 ; Krause, Vincent 3

1 Faculty of Informatics, University of Debrecen, Pf. 12, 4010 Debrecen, Hungary
2 Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
3 Keltenstr. 19, 41462 Neuss, Germany 
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     title = {Operator scaled {Wiener} bridges},
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     publisher = {EDP-Sciences},
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Barczy, Mátyás; Kern, Peter; Krause, Vincent. Operator scaled Wiener bridges. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 100-114. doi: 10.1051/ps/2014016

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