A decomposition of the bifractional Brownian motion and some applications. (English) Zbl 1157.60313

Summary: We have shown a decomposition of the bifractional Brownian motion with parameters \(H,K\) into the sum of a fractional Brownian motion with Hurst parameter \(HK\) plus a stochastic process with absolutely continuous trajectories. Some applications of this decomposition are discussed.


60G15 Gaussian processes
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[1] Decreusefond, L.; Üstünel, A. S., Stochastic analysis of the fractional Brownian motion, Potential Anal., 10, 177-214 (1999) · Zbl 0924.60034
[2] Es-Sebaiy, K.; Tudor, C. A., Multidimensional bifractional Brownian motion: Itô and Tanaka’s formulas, Stoch. Dyn., 3, 365-388 (2007) · Zbl 1139.60321
[3] Houdré, C.; Villa, J., An example of infinite dimensional quasi-helix, Contemp. Math., 366, 195-201 (2003) · Zbl 1046.60033
[4] Jolis, M., On the Wiener integral with respect to the fractional Brownian motion on an interval, J. Math. Anal. Appl., 330, 1115-1127 (2007) · Zbl 1185.60057
[5] Kahane, J. P., Helices at quasi-helices, Adv. Math., 7B, 417-433 (1981) · Zbl 0472.43005
[6] Kahane, J. P., Some Random Series of Functions (1985), Cambridge University Press · Zbl 0571.60002
[7] Kruk, I.; Russo, F.; Tudor, C. A., Wiener integrals, Malliavin calculus and covariance structure measure, J. Funct. Anal., 249, 92-142 (2007) · Zbl 1126.60046
[8] Monrad, D.; Rootzén, H., Small values of Gaussian processes and functional laws of the iterated logarithm, Probab. Theory Related Fields, 101, 173-192 (1995) · Zbl 0821.60043
[9] Nualart, D., Stochastic integration with respect to fractional Brownian motion and applications, Contemp. Math., 336, 3-39 (2003) · Zbl 1063.60080
[10] Nualart, D., The Malliavin Calculus and Related Topics (2006), Springer Verlag · Zbl 1099.60003
[11] Pipiras, V.; Taqqu, M. S., Are classes of deterministic integrands for fractional Brownian motion on an interval complete, Bernoulli, 6, 873-897 (2001) · Zbl 1003.60055
[12] Rogers, L. C.G., Arbitrage with fractional Brownian motion, Math. Finance, 7, 95-105 (1997) · Zbl 0884.90045
[13] Russo, F.; Tudor, C. A., On the bifractional Brownian motion, Stoch. Process. Appl., 5, 830-856 (2006) · Zbl 1100.60019
[14] Tudor, C. A.; Xiao, Y., Sample path properties of bifractional Brownian motion, Bernoulli, 13, 1023-1052 (2007) · Zbl 1132.60034
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