Free Access
Issue
ESAIM: PS
Volume 24, 2020
Page(s) 315 - 340
DOI https://doi.org/10.1051/ps/2020006
Published online 27 July 2020
  1. R.J. Adler and J.E. Taylor, Random Fields and Geometry. Springer, New York (2007). [Google Scholar]
  2. V. Anh, N. Leonenko, A. Olenko and V. Vaskovych, On rate of convergence in non-central limit theorems. Bernoulli 25 (2019) 2920–2948. [CrossRef] [Google Scholar]
  3. F. Avram, N. Leonenko and L. Sakhno, On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields. ESAIM: P&S 14 (2010) 210–255. [CrossRef] [Google Scholar]
  4. N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation. Cambridge University Press, Cambridge (1987). [CrossRef] [Google Scholar]
  5. L. Brandolini, S. Hofmann and A. Iosevich, Sharp rate of average decay of the Fourier transform of a bounded set. Geom. Funct. Anal. 13 (2003) 671–680. [CrossRef] [Google Scholar]
  6. A. Bulinski, E. Spodarev and F. Timmermann, Central limit theorems for the excursion set volumes of weakly dependent random fields. Bernoulli 18 (2012) 100–118. [CrossRef] [Google Scholar]
  7. R.M. Corless, G.H. Gonnet, D.E. Hare, D.J. Jeffrey and D.E. Knuth, On the LambertW function. Adv. Comput. Math. 5 (1996) 329–359. [Google Scholar]
  8. Y.A. Davydov, On distance in total variation between image measures. Stat. Probab. Lett. 129 (2017) 393–400. [Google Scholar]
  9. Y.A. Davydov and G.V. Martynova, Limit behavior of multiple stochastic integral, in Statistics and control of random process. Nauka, Moscow (1987) 55–57. [Google Scholar]
  10. R.L. Dobrushin and P. Major, Non-central limit theorems for nonlinear functionals of Gaussian fields. Z. Wahrsch. Verw. Gebiete 50 (1979) 27–52. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Doukhan, G. Oppenheim and M.S. Taqqu, Long-Range Dependence: Theory and Applications. Birkhäuser, Boston (2003). [Google Scholar]
  12. A. Iosevich and M. Rudnev, Freiman theorem, Fourier transform and additive structure of measures. J. Aust. Math. Soc. 86 (2009) 97–109. [CrossRef] [Google Scholar]
  13. A. Iosevich and E. Liflyand, Decay of the Fourier Transform: Analytic and Geometric Aspects. Birkhäuser, Basel (2014). [Google Scholar]
  14. K. Itô, Multiple Wiener integral. J. Math. Soc. Japan 3 (1951) 157–169. [CrossRef] [Google Scholar]
  15. A.V. Ivanov and N.N. Leonenko, Statistical Analysis of Random Fields. Kluwer Academic Publishers, Dordrecht (1989). [CrossRef] [Google Scholar]
  16. N. Leonenko, Limit Theorems for Random Fields with Singular Spectrum. Kluwer Academic Publishers, Dordrecht (1999). [CrossRef] [Google Scholar]
  17. N. Leonenko and A. Olenko, Tauberian and Abelian theorems for long-range dependent random fields. Methodol. Comput. Appl. Probab. 15 (2013) 715–742. [Google Scholar]
  18. N. Leonenko and A. Olenko, Sojourn measures of Student and Fisher-Snedecor random fields. Bernoulli 20 (2014) 1454–1483. [CrossRef] [Google Scholar]
  19. N. Leonenko and M.D. Ruiz-Medina, Increasing domain asymptotics for the first Minkowski functional of spherical random fields. Theory Probab. Math. Statist. 97 (2017) 120–141. [Google Scholar]
  20. N.N. Leonenko, M.D. Ruiz-Medina and M.S. Taqqu, Rosenblatt distribution subordinated to Gaussian random fields with long-range dependence. Stoch. Anal. Appl. 35 (2017) 144–177. [Google Scholar]
  21. P. Major, Multiple Wiener-Itô integrals. Springer, Berlin (1981). [CrossRef] [Google Scholar]
  22. D. Marinucci, Testing for non-Gaussianity on cosmic microwave background radiation: A review. Statist. Sci. 19 (2004) 294–307. [CrossRef] [Google Scholar]
  23. I. Nourdin and G. Poly, Convergence in total variation on Wiener chaos. Stoch. Process. Appl. 123 (2013) 651–674. [CrossRef] [Google Scholar]
  24. I. Nourdin, G. Peccati, G. Poly and R. Simone, Multidimensional limit theorems for homogeneous sums: a survey and a general transfer principle. ESAIM: P&S 20 (2016) 293–308. [CrossRef] [Google Scholar]
  25. D. Novikov, J. Schmalzing and V.F. Mukhanov, On non-Gaussianity in the cosmic microwave background. Astronom. Astrophys. 364 (2000) 17–25. [Google Scholar]
  26. A. Olenko, Limit theorems for weighted functionals of cyclical long-range dependent random fields. Stoch. Anal. Appl. 31 (2013) 199–213. [Google Scholar]
  27. G. Peccati and M.S. Taqqu, Wiener Chaos: Moments, Cumulants and Diagrams. A Survey with Computer Implementation. Springer, Berlin (2011). [CrossRef] [Google Scholar]
  28. V. Petrov, Limit Theorems of Probability Theory. Oxford University Press, New York (1995). [Google Scholar]
  29. J.B. Reyes and R.A. Blaya, Cauchy transform and rectifiability in Clifford analysis. Z. Anal. Anwendungen 24 (2005) 167–178. [CrossRef] [Google Scholar]
  30. E. Seneta, Regularly Varying Functions. Springer-Verlag, Berlin (1976). [CrossRef] [Google Scholar]
  31. M.S. Taqqu, Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. Verw. Gebiete 31 (1975) 287–302. [CrossRef] [Google Scholar]
  32. M.S. Taqqu, Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrsch. Verw. Gebiete 50 (1979) 53–83. [CrossRef] [MathSciNet] [Google Scholar]
  33. H. Wackernagel, Multivariate Geostatistics. Springer-Verlag, Berlin (1998). [CrossRef] [Google Scholar]
  34. G.I. Zelenov, On distances between distributions of polynomials. Theory Stoch. Process. 22 (2017) 79–85. [Google Scholar]
  35. R. Zintout, The total variation distance between two double Wiener-Itô integrals. Stat. Probab. Lett. 83 (2013) 2160–2167. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.