117
Views
15
CrossRef citations to date
0
Altmetric
Original Article

An Approximation of Subfractional Brownian Motion

&
Pages 1873-1886 | Received 16 May 2012, Accepted 17 Jan 2013, Published online: 10 Apr 2014

References

  • Bardina, X., Bascompte, D. (2010). Weak convergence towards two independent Gaussian process from a unique poisson process. Collect. Math. 61:191–204.
  • Billingsley, P. (1968). Convergence of Probability Measures, New York: Wiley.
  • Bojdecki, T., Gorostiza, L.G., Talarczyk, A. (2004). Sub-fractional Brownian motion and its relation to occupation times. Statist. Probab. Lett. 69:405–419.
  • Bojdecki, T., Gorostiza, L.G., Talarczyk, A. (2004). Fractional Brownian density process and its self-intersection local time of order k. J. Theoret. Probab. 69:717–739.
  • Bojdecki, T., Gorostiza, L.G., Talarczyk, A. (2006). Limit theorems for occupation time fluctuations of branching systems 1:long-range dependence. Stochastic Process. Appl. 116:1–18.
  • Bojdecki, T., Gorostiza, L.G., Talarczyk, A. (2007). Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems. Electron. Commun. Probab. 12:161–172.
  • Bojdecki, T., Gorostiza, L.G., Talarczyk, A. (2010). Particle systems with quasi-homogeneous initial states and their occupation time fluctuations. Electron. Commun. Probab. 15:191–202.
  • Borovskikh, Y.V., Korolyuk, V.S. (1997). Martingale Approximation, The Netherlands: VSP Utrecht.
  • Chen, C., Sun, L., Yan, L. (2012). An approximation to the Rosenblatt process using martingale differences. Statist. Probab. Lett. 82:748–757.
  • Davydov, Y. (1970). The invariance principle for stationary processes. Teor. Verojatn. Primen. 15:498–509.
  • Decreusefond, L., Üstünel, A.S. (1999). Stochastic analysis of the fractional Brownian motion. Potent. Anal. 10:177–214.
  • Delgado, R., Jolis, M. (2000). Weak approximation for a class of Gaussian process. J. Appl. Probab. 37:400–407.
  • Dzhaparidze, K., Van Zanten, H. (2004). A series expansion of fractional Brownian motion. Probab. Theory Relat. Fields. 103:39–55.
  • El-Nouty, C. (2012). The lower classes of the sub-fractional Brownian motion, In Stochastic Differential Equations and Processes. Springer Proc. Math. 7:179–196.
  • Enriquez, N. (2004). A simple construction of the fractional Brownian motion. Stochastic Process. Appl. 109:203–223.
  • Garzón, J., Gorostiza, L.G., León, J.A. (2012). A strong uniform approximation of sub-fractional Brownian motion. arXiv: 1202.1798.
  • Hall, P., Heyde, C.C. (1980) Martingale Limit Theorem and Application. Michigan: Academic Press.
  • Harnett, D., Nualart, D. (2012). Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes. Stochastic Process. Appl. 122:3460–3505.
  • Liu, J., Yan, L. (2012). Remarks on asymptotic behavior of weighted quadratic variation of subfractional Brownian motion. J. Kor. Statist. Soc. 41:177–187.
  • Li, Y., Dai, H. (2011). Approximations of fractional Brownian motion. Bernoulli. 17(4, 1195–1216.
  • Nieminen, A. (2004). Fractional Brownian motion and Martingale differences. Statist. Probab. Lett. 70:1–10.
  • Samko, S.G., Kilbas, A.A., Marichev, O.I. (1993). Fractional Integrals and Fractional Derivatives. New York: Gordan and Breach Science.
  • Shen, G., Yan, L. (2011). Remarks on sub-fractional Bessel Precesses. Acta Math. Sci. 31B(5): 1860–1876.
  • Shen, G., Yan, L. (2011). Remarks on an integral functional driven by sub-fractional Brownian motion. J. Kor. Statist. Soc.40:337–346.
  • Shen, G., Chen, C. (2012). Stochastic integration with respect to the sub-fractional Brownian motion with . Statist. Probab. Lett. 82:240–251.
  • Sottinen, T. (2001). Fractional Brownian motion, random walks and binary market models. Finan. Stochast. 5:343–355.
  • Taqqu, M.S. (1975). Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. Verw. Gebiete. 31:287–302.
  • Tudor, C. (2007). Some properties of the sub-fractional Brownian motion. Stochastics 79:431–448.
  • Tudor, C. (2011). Berry-Esséen bounds and almost sure CLT for the quadratic variation of the subfractional Brownian motion. J. Math. Anal. Appl. 375:667–676.
  • Tudor, C. (2009). On the Wiener integral with respect to a sub-fractional Brownian motion on an interval. J. Math. Anal. Appl. 351:456–468.
  • Yan, L., Shen, G. (2010). On the collision local time of sub-fractional Brownian Motions. Statist. Probab. Lett. 80:296–308.
  • Yan, L., Shen, G., He, K. (2011). Itô's formula for the subfractional Brownian motion. Commun. Stoch. Anal. 5:135–159.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.