References
- T. Bojdecki, L.G. Gorostiza, and A. Talarczyk, Sub-fractional Brownian motion and its relation to occupation times, Statist. Probab. Lett. 69 (2004), pp. 405–419.
- S. Chatterjee, An error bound in the Sudakov--Fernique inequality, preprint (2005), arXiv:math/0510424.
- H. Chernoff, Sequential tests for the mean of a normal distribution IV (Discrete case), Ann. Math. Statist. 36 (1965), pp. 55–68.
- R.B. Davies and D.S. Harte, Tests for Hurst effect, Biometrika 74 (1987), pp. 95–102.
- K. Debicki and P. Kisowski, A note on upper estimates for Pickands constants, Statist. Probab. Lett. 78 (2009), pp. 2046–2051.
- A.B. Dieker and B. Yakir, On asymptotic constants in the theory of extremes for Gaussian processes, Bernoulli 20 (2014), pp. 1600–1619.
- R.M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Funct. Anal. 1 (1967), pp. 290–330.
- X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiens [Regularity of the paths of Gaussian random functions], in École d’Été de Probabilités de Saint-Flour, IV-1974 [Summer School Probability of Saint-Flour], Vol. 480, Lecture Notes in Mathematics, Springer, Berlin, 1975. pp. 1–96.
- A. Harper, Pickands’ constant Hα does not equal 1/Γ(1/α), for small α, preprint (2014), arXiv:1404.5505.
- C. Houdré and J. Villa, An example of infinite dimensional quasi-helix, Contemp. Math. 336 (2003), pp. 195–202.
- R. Ivanov and V. Piterbarg, Connecting discrete and continuous path-dependent options for a fractional Brownian motion, preprint (2004),
- C. Jost, Transformation formulas for fractional Brownian motion, Stochastic Process. Appl. 116 (2006), pp. 1341–1357.
- J.-P. Kahane, Hélices et quasi-hélices [Helices and quasi-helices], Adv. Math. Suppl. Stud. 7b (1981), pp. 417–433.
- J.-P. Kahane, Some Random Series of Functions, 2nd ed., Cambridge University Press, Cambridge, 1985.
- A.N. Kolmogorov, Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, C. R. (Doklady) Acad. Sci. URSS (N.S.). 26 (1940), pp. 115–118.
- P. Lei and D. Nualart, A decomposition of the bifractional Brownian motion and some applications, Statist. Probab. Lett. 79 (2009), pp. 619–624.
- M. Lifshits, Lectures on Gaussian Processes, Springer Briefs in Mathematics, Springer-Verlag, Heidelberg, 2012.
- Y.S. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Vol. 1929, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2008.
- A. Novikov and E. Valkeila, On some maximal inequalities for fractional Brownian motions, Statist. Probab. Lett. 44 (1999), pp. 47–54.
- G. Pisier, Conditions d’entropie assurant la continuité de certains processus et applications à l’analyse harmonique [Conditions on entropy ensuring the continuity of certain processes and applications to harmonic analysis], Séminaires Analyse fonctionnelle [Functional anlysis seminars] (dit "Maurey-Schwartz" [called "Marty-Schwartz"]). Exposés 13--14 (1979–1980), pp. 1–43.
- V.I. Piterbarg, Asymptotic Methods in the Theory of Gaussian Processes and Fields, Translations of Mathematical Monographs, 148, American Mathematical Society, Providence, RI, 1996.
- F. Russo and C.A. Tudor, On bifractional Brownian motion, Stochastic Process. Appl. 116 (2006), pp. 830–856.
- S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers, Yverdon, 1993.
- Q.-M. Shao, Bounds and estimators of a basic constant in extreme value theory of Gaussian processes, Statist. Sinica 6 (1996), pp. 245–257.
- D. Siegmund, Corrected diffusion approximations in certain random walk problems, Adv. Appl. Probab. 11 (1979), pp. 701–719.
- T. Sottinen and L. Viitasaari, Stochastic analysis of Gaussian processes via Fredholm representation, preprint (2014), arXiv:1410.2230.
- V.N. Sudakov, Geometric Problems in the Theory of Infinite-dimensional Probability Distributions, Proc. Steklov Inst. Math. 2 (1979), pp. 1–178.
- M. Talagrand, Sharper bounds for Gaussian and empirical processes, Ann. Probab. 22 (1994), pp. 28–76.
- M. Talagrand, The Generic Chaining. Upper and Lower Bounds of Stochastic Processes, Springer, Berlin, 2005.
- M. Talagrand, Upper and lower bounds for stochastic processes. Modern methods and classical problems, Springer, Heidelberg, 2014.
- R.A. Vitale, Some comparisons for Gaussian processes, Proc. Am. Math. Soc. 128 (2000), pp. 3043–3046.
- A.T.A. Wood and G. Chan, Simulation of stationary Gaussian processes in [0,1]d, J. Comput. Graph. Statist. 3 (1994), pp. 409–432.