References

THE LAW OF A STOCHASTIC INTEGRAL WITH RESPECT TO SUBFRACTIONAL BROWNIAN MOTIONS


[1] E. Alòs, O. Mazet and D. Nualart, Stochastic calculus with respect to Gaussian processes, Ann. Probab. 29 (2001), 766-801.

[2] X. Bardina and C. A. Tudor, The law of a stochastic integral with two independent fractional Brownian motions, Bol. Soc. Mat. Mex. III. Ser. 13(1) (2007), 231-242.

[3] R. Berthuet, Loi du logharitme itéré pour cetaines intégrales stochastiques, Ann. Sci. Univ. Clérmont-Ferrand Math. 69 (1981), 9-18.

[4] F. Biagini, Y. Hu, B. Øksendal and T. Zhang, Stochastic Calculus for fBm and Applications, Springer-Verlag, (2008).

[5] T. Bojdecki, L. Gorostiza and A. Talarczyk, Sub-fractional Brownian motion and its relation to occupation times, Statist. Probab. Lett. 69 (2004), 405-419.

[6] T. Bojdecki, L. Gorostiza and A. Talarczyk, Some extension of fractional Brownian motion and sub-fractional Brownian motion related to particle systems, Elect. Comm. Probab. 12 (2007), 161-172.

[7] P. Caithamer, Decoupled double stochastic fractional integrals, Stochastics and Stochastics Reports 77 (2005), 205-210.

[8] Y. Hu, Integral transformations and anticipative calculus for fBms, Memoirs Amer. Math. Soc. 175 (2005), 825.

[9] O. Julià and D. Nualart, The distribution of a double stochastic integral with respect to two independent Brownian sheets, Stochastics 25 (1998), 171-182.

[10] P. Lévy, Wiener’s random functions, and other Laplacian random functions, Proc. 2nd Berkeley Symp. Math. Stat. Probab., University of California Press, Berkeley, Ca. 2 (1951).

[11] Y. Mishura, Stochastic calculus for fBms and related processes, Lect. Notes in Math. 1929 (2008).

[12] D. Nualart, On the distribution of a double stochastic integral, Z. Wahrsch. Verw. Gebiete 65 (1983), 49-60.

[13] D. Nualart, Malliavin Calculus and Related Topics, 2nd edition, Springer, New York, (2006).

[14] E. Philip Protter, Stochastic Integration and Differential Equations, 2nd edition, Springer-Verlag, New York, 2005.

[15] C. Tudor, Some properties of the sub-fractional Brownian motion, Stochastics 79 (2007), 431-448.

[16] C. Tudor, Inner product spaces of integrands associated to sub-fractional Brownian motion, Statist. Probab. Lett. 78 (2008), 2201-2209.

[17] C. Tudor, Multiple sub-fractional integrals and some approximations, Appl. Anal. 87 (2008), 311-323.

[18] C. Tudor, Some aspects of stochastic calculus for the sub-fractional Brownian motion, An. Univ. Bucur. Mat. 57(2) (2008), 199-230.

[19] C. Tudor, On the Wiener integral with respect to a sub-fractional Brownian motion, J. Math. Anal. Appl. 351 (2009), 456-468.

[20] L. Yan and C. Chen, Intersection local time and calculus for Lévy area process, submitted (2009).

[21] L. Yan and G. Shen, Itô and Tanaka formula for sub-fractional Brownian motion, submitted (2009).

[22] M. Yor, Remarques sur une formule de Paul Lévy, Lect. Notes in Math. 784 (1978), 343-346.