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Multidimensional bifractional Brownian motion: Itô and Tanaka formulas. (English) Zbl 1139.60321

Summary: Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals, we derive Itô’s and Tanaka’s formulas for the \(d\)-dimensional bifractional Brownian motion.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
60G15 Gaussian processes
60G12 General second-order stochastic processes
60H05 Stochastic integrals
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References:

[1] Alòs E., Ann. Probab. 29 pp 766–
[2] DOI: 10.1007/978-1-4471-0873-3_2 · doi:10.1007/978-1-4471-0873-3_2
[3] DOI: 10.1111/j.1467-9892.2006.00494.x · Zbl 1164.62034 · doi:10.1111/j.1467-9892.2006.00494.x
[4] Begyn A., Electronic J. Probab. 10 pp 691– · Zbl 1109.60024 · doi:10.1214/EJP.v10-245
[5] DOI: 10.1016/j.spl.2004.06.035 · Zbl 1076.60027 · doi:10.1016/j.spl.2004.06.035
[6] DOI: 10.1016/S0304-4149(01)00085-0 · Zbl 1053.60055 · doi:10.1016/S0304-4149(01)00085-0
[7] DOI: 10.1023/A:1008634027843 · Zbl 0924.60034 · doi:10.1023/A:1008634027843
[8] DOI: 10.1137/S036301299834171X · Zbl 0947.60061 · doi:10.1137/S036301299834171X
[9] DOI: 10.1081/SAP-200050121 · Zbl 1067.60026 · doi:10.1081/SAP-200050121
[10] DOI: 10.1016/j.anihpb.2004.06.002 · Zbl 1083.60045 · doi:10.1016/j.anihpb.2004.06.002
[11] DOI: 10.1090/conm/336/06034 · doi:10.1090/conm/336/06034
[12] DOI: 10.1007/BF01311348 · Zbl 0794.60046 · doi:10.1007/BF01311348
[13] Kuo H. H., White Noise Distribution Theory (1996)
[14] DOI: 10.1007/978-1-4757-2437-0 · doi:10.1007/978-1-4757-2437-0
[15] DOI: 10.1007/s440-000-8016-7 · doi:10.1007/s440-000-8016-7
[16] Russo F., Stoch. Process. Appl. 5 pp 830–
[17] DOI: 10.1023/B:JOTP.0000020698.51262.24 · Zbl 1055.60073 · doi:10.1023/B:JOTP.0000020698.51262.24
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