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References

  1. Ayache, Antoine; Linde, Werner. Approximation of Gaussian random fields: general results and optimal wavelet representation of the Lévy fractional motion. J. Theoret. Probab. 21 (2008), no. 1, 69--96. MR2384473 (2009c:60127)
  2. Ayache, Antoine; Taqqu, Murad S. Rate optimality of wavelet series approximations of fractional Brownian motion. J. Fourier Anal. Appl. 9 (2003), no. 5, 451--471. MR2027888 (2004m:60084)
  3. Belinsky, Eduard; Linde, Werner. Small ball probabilities of fractional Brownian sheets via fractional integration operators. J. Theoret. Probab. 15 (2002), no. 3, 589--612. MR1922439 (2004d:60092)
  4. Carl, Bernd; Stephani, Irmtraud. Entropy, compactness and the approximation of operators.Cambridge Tracts in Mathematics, 98. Cambridge University Press, Cambridge, 1990. x+277 pp. ISBN: 0-521-33011-4 MR1098497 (92e:47002)
  5. Dzhaparidze, Kacha; van Zanten, Harry. Optimality of an explicit series expansion of the fractional Brownian sheet. Statist. Probab. Lett. 71 (2005), no. 4, 295--301. MR2145497 (2006g:60057)
  6. Fernique, Xavier. Fonctions aléatoires gaussiennes, vecteurs aléatoires gaussiens.(French) [Gaussian random functions, Gaussian random vectors] Université de Montréal, Centre de Recherches Mathématiques, Montreal, QC, 1997. iv+217 pp. ISBN: 2-921120-28-3 MR1472975 (99f:60078)
  7. Gilsing, Hagen; Sottinen, Tommi. Power series expansions for fractional Brownian motions. Theory Stoch. Process. 9 (2003), no. 3-4, 38--49. MR2306058
  8. Iglói, E. A rate-optimal trigonometric series expansion of the fractional Brownian motion. Electron. J. Probab. 10 (2005), no. 41, 1381--1397 (electronic). MR2183006 (2006f:60039)
  9. Kühn, Thomas; Linde, Werner. Optimal series representation of fractional Brownian sheets. Bernoulli 8 (2002), no. 5, 669--696. MR1935652 (2003m:60131)
  10. Ledoux, Michel. Isoperimetry and Gaussian analysis. Lectures on probability theory and statistics (Saint-Flour, 1994), 165--294, Lecture Notes in Math., 1648, Springer, Berlin, 1996. MR1600888 (99h:60002)
  11. Kwapień, Stanisƚaw; Woyczyński, Wojbor A. Random series and stochastic integrals: single and multiple.Probability and its Applications. Birkhäuser Boston, Inc., Boston, MA, 1992. xvi+360 pp. ISBN: 0-8176-3572-6 MR1167198 (94k:60074)
  12. Li, Wenbo V.; Linde, Werner. Approximation, metric entropy and small ball estimates for Gaussian measures. Ann. Probab. 27 (1999), no. 3, 1556--1578. MR1733160 (2001c:60059)
  13. Li, W. V.; Shao, Q.-M. Gaussian processes: inequalities, small ball probabilities and applications. Stochastic processes: theory and methods, 533--597, Handbook of Statist., 19, North-Holland, Amsterdam, 2001. MR1861734
  14. Lifshits, M. A. On Haar expansion of Riemann--Liouville process in a critical case. Available at arXiv:0910.2177 (2009).
  15. Lifshits, Mikhail A.; Linde, Werner; Shi, Zhan. Small deviations of Riemann-Liouville processes in $Lsb q$-spaces with respect to fractal measures. Proc. London Math. Soc. (3) 92 (2006), no. 1, 224--250. MR2192391 (2006m:60053)
  16. Lifshits, Mikhail; Simon, Thomas. Small deviations for fractional stable processes. Ann. Inst. H. Poincaré Probab. Statist. 41 (2005), no. 4, 725--752. MR2144231 (2006d:60081)
  17. Luschgy, Harald; Pagès, Gilles. High-resolution product quantization for Gaussian processes under sup-norm distortion. Bernoulli 13 (2007), no. 3, 653--671. MR2348745 (2009d:60111)
  18. Luschgy, Harald; Pagès, Gilles. Expansions for Gaussian processes and Parseval frames. Electron. J. Probab. 14 (2009), no. 42, 1198--1221. MR2511282
  19. Malyarenko, Anatoliy. An optimal series expansion of the multiparameter fractional Brownian motion. J. Theoret. Probab. 21 (2008), no. 2, 459--475. MR2391256 (2009j:60082)
  20. Pisier, Gilles. The volume of convex bodies and Banach space geometry.Cambridge Tracts in Mathematics, 94. Cambridge University Press, Cambridge, 1989. xvi+250 pp. ISBN: 0-521-36465-5; 0-521-66635-X MR1036275 (91d:52005)
  21. Schack, H. An optimal wavelet series expansion of the Riemann--Liouville process. To appear J. Theoret. Probab.
  22. Zygmund, A. Trigonometric Series. Cambridge Univ. Press, Cambridge, 1950.
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