Free Access
Volume 19, 2015
Page(s) 766 - 781
Published online 18 December 2015
  1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. Dover Publ., New York (1972). [Google Scholar]
  2. X. Bardina and K. Es-Sebaiy, An extension of bifractional Brownian motion. Commun. Stoch. Anal. 5 (2011) 333–340. [MathSciNet] [Google Scholar]
  3. O.E. Barndorff-Nielsen and V. Perez-Abreu, Stationary and selfsimilar processes driven by Lévy processes. Stochastic Processes Appl. 84 (1999) 357–369. [CrossRef] [Google Scholar]
  4. T. Bojdecki, L.G. Gorostiza and A. Talarczyk, Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems. Electron. Commun. Probab. 12 (2007) 161–172. [CrossRef] [Google Scholar]
  5. P. Cheredito, W. Kawaguchi and M. Maejima, Fractional Ornstein–Uhlenbeck processes. Electron. J. Probab. 8 (2003) 1–14. [MathSciNet] [Google Scholar]
  6. M. Lifshits and S. Cohen, Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres. ESAIM: PS 16 (2012) 165–221. [CrossRef] [EDP Sciences] [Google Scholar]
  7. D.S. Egorov, Annual student’s memoir. St. Petersburg State University (2014). [Google Scholar]
  8. P. Embrechts and M. Maejima, Selfsimilar Processes. Princeton University Press (2002). [Google Scholar]
  9. C. Houdré and J. Villa, An example of infinite dimensional quasi-helix. Stochastic Models. Ser.: Contemp. Math. 336 (2003) 195–201. [CrossRef] [Google Scholar]
  10. P. Lei and D. Nualart, A decomposition of the bifractional Brownian motion and some applications. Stat. Probab. Lett. 79 (2009) 619–624. [CrossRef] [Google Scholar]
  11. M. Lifshits, Random Processes by Example. World Scientific, Singapore (2014). [Google Scholar]
  12. M. Lifshits and K. Volkova, Bifractional Brownian motion: existence and border cases. Preprint arXiv:1502.02217 (2015). [Google Scholar]
  13. M.A. Lifshits, R. Schilling and I. Tyurin, A probabilistic inequality related to negative definite functions, in High Dimensional Probability VI, Vol. 66 of Ser. Progress in Probability, edited by C. Houdré et al. Birkhäuser, Basel. Preprint: arXiv:1205.1284 (2013). [Google Scholar]
  14. C. Ma, The Schoenberg–Lévy kernel and relationships among fractional Brownian motion, bifractional Brownian motion and others. Theory Probab. Appl. 57 (2013) 619–632. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Marouby, Micropulses and different types of Brownian motion. J. Appl. Probab. 48, (2011) 792–810. [CrossRef] [MathSciNet] [Google Scholar]
  16. R. Schilling, R. Song and Z. Vondraček, Bernstein Functions. De Gruyter, Berlin. Stud. Math. (2010) 37. [Google Scholar]
  17. G. Samorodnitsky and M.S. Taqqu, Stable Non-Gaussian Random Processes. Chapman & Hall, New York (1994). [Google Scholar]
  18. C.A. Tudor and Y. Xiao, Sample path properties of bifractional Brownian motion. Bernoulli 13 (2007) 1023–1052. [CrossRef] [MathSciNet] [Google Scholar]
  19. W. Wang, On p-variation of bifractional Brownian motion. Appl. Math. J. Chinese Univ. 26 (2011) 127–141. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.