Bifractional Brownian motion (bfBm) is a centered Gaussian process with covariance
We study the existence of bfBm for a given pair of parameters and encounter some related limiting processes.
Mots-clés : Bifractional Brownian motion, Gaussian process, fractional Brownian motion
@article{PS_2015__19__766_0, author = {Lifshits, Mikhail and Volkova, Ksenia}, title = {Bifractional {Brownian} motion: existence and border cases}, journal = {ESAIM: Probability and Statistics}, pages = {766--781}, publisher = {EDP-Sciences}, volume = {19}, year = {2015}, doi = {10.1051/ps/2015015}, zbl = {1333.60075}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2015015/} }
TY - JOUR AU - Lifshits, Mikhail AU - Volkova, Ksenia TI - Bifractional Brownian motion: existence and border cases JO - ESAIM: Probability and Statistics PY - 2015 SP - 766 EP - 781 VL - 19 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2015015/ DO - 10.1051/ps/2015015 LA - en ID - PS_2015__19__766_0 ER -
%0 Journal Article %A Lifshits, Mikhail %A Volkova, Ksenia %T Bifractional Brownian motion: existence and border cases %J ESAIM: Probability and Statistics %D 2015 %P 766-781 %V 19 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2015015/ %R 10.1051/ps/2015015 %G en %F PS_2015__19__766_0
Lifshits, Mikhail; Volkova, Ksenia. Bifractional Brownian motion: existence and border cases. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 766-781. doi : 10.1051/ps/2015015. http://archive.numdam.org/articles/10.1051/ps/2015015/
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. Dover Publ., New York (1972).
An extension of bifractional Brownian motion. Commun. Stoch. Anal. 5 (2011) 333–340. | Zbl
and ,Stationary and selfsimilar processes driven by Lévy processes. Stochastic Processes Appl. 84 (1999) 357–369. | Zbl
and ,Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems. Electron. Commun. Probab. 12 (2007) 161–172. | Zbl
, and ,Fractional Ornstein–Uhlenbeck processes. Electron. J. Probab. 8 (2003) 1–14. | Zbl
, and ,Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres. ESAIM: PS 16 (2012) 165–221. | Zbl
and ,D.S. Egorov, Annual student’s memoir. St. Petersburg State University (2014).
P. Embrechts and M. Maejima, Selfsimilar Processes. Princeton University Press (2002). | Zbl
An example of infinite dimensional quasi-helix. Stochastic Models. Ser.: Contemp. Math. 336 (2003) 195–201. | Zbl
and ,A decomposition of the bifractional Brownian motion and some applications. Stat. Probab. Lett. 79 (2009) 619–624. | Zbl
and ,M. Lifshits, Random Processes by Example. World Scientific, Singapore (2014). | Zbl
M. Lifshits and K. Volkova, Bifractional Brownian motion: existence and border cases. Preprint arXiv:1502.02217 (2015).
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). | Zbl
The Schoenberg–Lévy kernel and relationships among fractional Brownian motion, bifractional Brownian motion and others. Theory Probab. Appl. 57 (2013) 619–632. | Zbl
,Micropulses and different types of Brownian motion. J. Appl. Probab. 48, (2011) 792–810. | Zbl
,Bernstein Functions. De Gruyter, Berlin. Stud. Math. (2010) 37. | Zbl
, and ,G. Samorodnitsky and M.S. Taqqu, Stable Non-Gaussian Random Processes. Chapman & Hall, New York (1994). | Zbl
Sample path properties of bifractional Brownian motion. Bernoulli 13 (2007) 1023–1052. | Zbl
and ,On -variation of bifractional Brownian motion. Appl. Math. J. Chinese Univ. 26 (2011) 127–141. | Zbl
,Cité par Sources :