Large deviations for functionals of some self-similar Gaussian processes

References

• D. Alpay and D. Levanony, On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions, Potential Anal. 28(2) (2008), pp. 163–184. doi: 10.1007/s11118-007-9070-4
   Web of Science ®Google Scholar
• N. Aronszajn, Theory of reproducing kernels, Trans. Am. Math. Soc. 68 (1950), pp. 337–404. doi: 10.1090/S0002-9947-1950-0051437-7
   Web of Science ®Google Scholar
• R. Bass, X. Chen, and J. Rosen, Large deviations for Riesz potentials of additive processes, Ann. Inst. Henri Poincaré Probab. Stat. 45(3) (2009), pp. 626–666. doi: 10.1214/08-AIHP181
   Web of Science ®Google Scholar
• S.M. Berman, Local times and sample function properties of stationary Gaussian processes, Trans. Am. Math. Soc. 137 (1969), pp. 277–299. doi: 10.1090/S0002-9947-1969-0239652-5
   Web of Science ®Google Scholar
• S.M. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 (1973/74), pp. 69–94. doi: 10.1512/iumj.1974.23.23006
   Web of Science ®Google Scholar
• F. Biagini, Y. Hu, B. Øksendal, and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications, Probability and its Applications (New York), Springer-Verlag London, Ltd., London, 2008.
   Google Scholar
• T. Bojdecki, L.G. Gorostiza, and A. Talarczyk, Sub-fractional Brownian motion and its relation to occupation times, Statist. Probab. Lett. 69(4) (2004), pp. 405–419. doi: 10.1016/j.spl.2004.06.035
   Web of Science ®Google Scholar
• X. Chen, Large deviations and laws of the iterated logarithm for the local times of additive stable processes, Ann. Probab. 35(2) (2007), pp. 602–648. doi: 10.1214/009117906000000601
   Web of Science ®Google Scholar
• X. Chen, Random Walk Intersections: Large Deviations and Related Topics, Mathematical Surveys and Monographs Vol. 157, American Mathematical Society, Providence, RI, 2010.
   Google Scholar
• X. Chen, W.V. Li, J. Rosiński, and Q.-M. Shao, Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes, Ann. Probab. 39(2) (2011), pp. 729–778. doi: 10.1214/10-AOP566
   Web of Science ®Google Scholar
• L. Decreusefond and A.S. Üstünel, Stochastic analysis of the fractional Brownian motion, Potential Anal. 10(2) (1999), pp. 177–214. doi: 10.1023/A:1008634027843
   Web of Science ®Google Scholar
• D. Harnett and D. Nualart, Decomposition and limit theorems for a class of self-similar Gaussian processes, in Stochastic analysis and related topics, Progr. Probab., Vol. 72, Birkhäuser/Springer, Cham, 2017, pp. 99–116.
   Google Scholar
• S. Janson, Gaussian Hilbert Spaces, Cambridge Tracts in Mathematics, Vol. 129, Cambridge University Press, Cambridge, 1997.
   Google Scholar
• W. König and P. Mörters, Brownian intersection local times: Upper tail asymptotics and thick points, Ann. Probab. 30(4) (2002), pp. 1605–1656. doi: 10.1214/aop/1039548368
   Web of Science ®Google Scholar
• P. Lei and D. Nualart, A decomposition of the bifractional Brownian motion and some applications, Statist. Probab. Lett. 79(5) (2009), pp. 619–624. doi: 10.1016/j.spl.2008.10.009
   Web of Science ®Google Scholar
• W.V. Li and Q.-M. Shao, Gaussian processes: Inequalities, small ball probabilities and applications, in Stochastic Processes: Theory and Methods, Handbook of Statist., Vol. 19, North-Holland, Amsterdam, 2001, pp. 533–597.
   Google Scholar
• N. Luan, Strong local non-determinism of sub-fractional Brownian motion, Applied Mathematics 6 (2015), pp. 2211-2216.
   Google Scholar
• B.B. Mandelbrot and J.W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10 (1968), pp. 422–437. doi: 10.1137/1010093
   Web of Science ®Google Scholar
• D. Nualart, The Malliavin Calculus and Related Topics, 2nd ed., Probability and its Applications (New York), Springer-Verlag, Berlin, 2006.
   Google Scholar
• J. Ruiz de Chávez and C. Tudor, A decomposition of sub-fractional Brownian motion, Math. Rep. (Bucur.) 11(61) (2009), pp. 67–74.
   Google Scholar
• S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, 1993. Theory and applications, Edited and with a foreword by S. M. Nikol'ski 1˘, Translated from the 1987 Russian original, Revised by the authors.
   Google Scholar
• G. Samorodnitsky and M.S. Taqqu, Stable Non-Gaussian Random Processes, Stochastic Modeling, Chapman & Hall, New York, 1994. Stochastic Models with Infinite Variance.
   Google Scholar
• C.A. Tudor and Y. Xiao, Sample path properties of bifractional Brownian motion, Bernoulli 13(4) (2007), pp. 1023–1052. doi: 10.3150/07-BEJ6110
   Web of Science ®Google Scholar
• A.W. van der Vaart and J.H. van Zanten, Reproducing kernel Hilbert spaces of Gaussian priors, in Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, Inst. Math. Stat. (IMS) Collect. Vol. 3, Inst. Math. Statist., Beachwood, OH, 2008, pp. 200–222.
   Google Scholar