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.
DOI : 10.1051/ps/2014016
Mots clés : Multidimensional Wiener bridge, operator scaling, strong law of large numbers, asymptotic behavior
@article{PS_2015__19__100_0, author = {Barczy, M\'aty\'as and Kern, Peter and Krause, Vincent}, title = {Operator scaled {Wiener} bridges}, journal = {ESAIM: Probability and Statistics}, pages = {100--114}, publisher = {EDP-Sciences}, volume = {19}, year = {2015}, doi = {10.1051/ps/2014016}, mrnumber = {3374871}, zbl = {1333.60116}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2014016/} }
TY - JOUR AU - Barczy, Mátyás AU - Kern, Peter AU - Krause, Vincent TI - Operator scaled Wiener bridges JO - ESAIM: Probability and Statistics PY - 2015 SP - 100 EP - 114 VL - 19 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2014016/ DO - 10.1051/ps/2014016 LA - en ID - PS_2015__19__100_0 ER -
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. http://www.numdam.org/articles/10.1051/ps/2014016/
Alpha-Wiener bridges: singularity of induced measures and sample path properties. Stochastic Anal. Appl. 28 (2010) 447–466. | MR | Zbl
and ,Arbitrage in stock index futures. J. Business 63 (1990) 7–31.
and ,I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed. Springer, Berlin (1991). | MR
H.-H. Kuo, Introduction to Stochastic Integration, Universitext. Springer, New York (2006). | MR | Zbl
On a one-parameter generalization of the Brownian bridge and associated quadratic functionals. J. Theor. Probab. 17 (2004) 1021–1029. | MR | Zbl
,M.M. Meerschaert and H.P. Scheffler, Limit Distributions for Sums of Independent Random Vectors. Wiley, New York (2001). | MR | Zbl
D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. 3rd ed., corr. 2nd printing. Springer, Berlin (2001). | MR | Zbl
Estimating the degree of interventionist policies in the run-up to EMU, Appl. Econ. 43 (2011) 207–218.
, and ,Estimating exchange rate dynamics with diffusion processes: an application to Greek EMU data. Empirical Econ. 33 (2007) 23–39.
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