Geodesic
On Haar expansion of Riemann–Liouville process in a critical case
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 171-180 
M. A. Lifshits. On Haar expansion of Riemann–Liouville process in a critical case. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 171-180. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a12/
@article{ZNSL_2009_368_a12,
     author = {M. A. Lifshits},
     title = {On {Haar} expansion of {Riemann{\textendash}Liouville} process in a~critical case},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {171--180},
     year = {2009},
     volume = {368},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a12/}
}
TY  - JOUR
AU  - M. A. Lifshits
TI  - On Haar expansion of Riemann–Liouville process in a critical case
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 171
EP  - 180
VL  - 368
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a12/
LA  - ru
ID  - ZNSL_2009_368_a12
ER  - 
%0 Journal Article
%A M. A. Lifshits
%T On Haar expansion of Riemann–Liouville process in a critical case
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 171-180
%V 368
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a12/
%G ru
%F ZNSL_2009_368_a12

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We show that Haar-based series representation of the critical Riemann–Liouville process $R^\alpha$ with $\alpha=3/2$ is rearrangement non-optimal in the sense of convergence rate in $\mathbf C[0,1]$. Bibl. – 10 titles.

[1] A. Ayache, W. Linde, “Series representations of fractional Gaussian processes by trigonometric and Haar systems”, Electronic J. Probab., 14 (2009) (to appear) | MR | Zbl

[2] A. Ayache, M. S. Taqqu, “Rate optimality of wavelet series approximations of fractional Brownian motion”, J. Fourier Anal. Appl., 9 (2003), 451–471 | DOI | MR | Zbl

[3] K. Dzhaparidze, H. van Zanten, “Optimality of an explicit series expansion of the fractional Brownian sheet”, Statist. Probab. Letters, 71 (2005), 295–301 | DOI | MR | Zbl

[4] H. Gilsing, T. Sottinen, “Power series expansions for fractional Brownian motions”, Theory of Stoch. Proc., 9:3–4 (2003), 38–49 | MR | Zbl

[5] E. Iglói, “A rate optimal trigonometric series expansion of the fractional Brownian motion”, Electronic J. Probab., 10 (2005), 1381–1397 | DOI | MR | Zbl

[6] Th. Kühn, W. Linde, “Optimal series representation of fractional Brownian sheets”, Bernoulli, 8 (2002), 669–696 | MR | Zbl

[7] M. A. Lifshits, Gaussian Random Functions, Kluwer, 1995 | MR | Zbl

[8] M. A. Lifshits, Th. Simon, “Small deviations for fractional stable processes”, Ann. Inst. H. Poincaré, 41 (2005), 725–752 | DOI | MR | Zbl

[9] A. Malyarenko, “An optimal series expansion of the multiparameter fractional Brownian motion”, J. Theoret. Probab., 21 (2008), 459–475 | DOI | MR | Zbl

[10] H. Schack, “An optimal wavelet series expansion of the Riemann–Liouville process”, J. Theoret. Probab. (to appear) | MR